Quadratic Function

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline x&f(x)\\\hline-1&4\\\hline0&12\\\hline1&22\\\hline\end{array}\\&\text{For the quadratic function }f,\text{the table shows three values of }x\text{ and their corresponding}\\&\text{values of }f(x).\text{Which equation defines }f?\end{aligned}\)

\(\begin{aligned}&\text{The variables }x\mathrm{~and~}y\text{ have a quadratic relationship. When }x=0,~y=45\text{. When }x=6,\\&y=81.\mathrm{~When~}x=15,y=0.\text{ Which equation represents this relationship?}\end{aligned}\)

\(\begin{aligned}
&\text{The graph of }y=2x^{2}+bx+c\mathrm{~is~shown,~where~}b\mathrm{~and~}c\text{ are constants. }\\&\text{What is the value of }bc?\end{aligned}\)

\(\mathrm{The~}x\text{-intercept of the graph shown is }(x,0).\text{ What is the value of }x\mathrm{?}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^2=(40)(40)\\&\text{What is the positive solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{x^2}{25}=36\\
&\text{What is a solution to the given equation}?
\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~k^2-53=91\\
&\text{What is the positive solution to the given equation}?
\end{aligned}\)

\(\begin{aligned}
&\text{If }t >0 \text{ and } t^2-4=0,\text {what is the value of }t?
\end{aligned}\)

\(\mathrm{If~}\frac{42}{x}=7x,\text{ what is the value of }7x^2?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v-12)(v-3)=0\\&\text{What are all possible solutions to the given equation?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~(d-30)(d+30)-7=-7\\
&\text{What is a solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^2-28x=0\\&\text{Which of the following is a solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~z^{2}+10z-24=0\\&\text{What is one of the solutions to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-4x^{2}-7x=-36\\&\text{What is the positive solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^{2}+x-12=0\\
&\mathrm{If~}a\text{ is a solution of the equation above and }a>0,\text{what is the value of }a?\end{aligned}\)

\(\mathrm{If~}121x^{2}=-110x+56,\text{ what is the value of }11x+5,\mathrm{~where~}11x+5>0?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x(x-15)=34\\&\text{What is the positive solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3x^2+x-5=0\\&\text{What is the greatest solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~w^{2}+12w-40=0\\
&\text{Which of the following is a solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^2+2x=72\\&\text{What is one of the solutions to the given equation?}
\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^{2}-2x-9=0\\
&\text{One solution to the given equation can be written as }1+\sqrt{k},\text{where }k\text{ is a constant.}\\&\text{What is the value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^2-4x-1=0\\
&\text{A solution to the given equation is }x=\sqrt{k}+2.\text{ What is the value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2x^{2}-8x-7=0\\
&\text{One solution to the given equation can be written as }\frac{8-\sqrt{k}}{4},\mathrm{~where~}k\text{ is a constant. }\\&\text{What is the value of } k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^{2}+11x+19=0\\
&\text{One solution to the given equation can be written as }\frac{-11-\sqrt{k}}{2},\mathrm{~where~}k\text{ is a constant. }\\&\text{What is the value of } k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^{2}+5x=37\\&\text{The solutions to the given equation are}\frac{m+\sqrt{q}}{2}\mathrm{~and~}\frac{m-\sqrt{q}}{2},\mathrm{~where~}m\mathrm{~and~}q\text{ are integers. What}\\&\text{is the value of }m+q?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2x^{2}-12x-13=0\\
&\text{One solution to the given equation can be written as }h-\frac{1}{2}\sqrt{k},\text{ where }h\text{ and }k \\&\text{are integer constants. What is the value of }h+k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-8x(x+9)=40\\
&\text{One solution to the given equation can be written as }x=-\frac{s+\sqrt{t}}{2},\mathrm{where~}s\mathrm{~and~}t\mathrm{~are}\\&\text{positive integers. What is the value of }\frac{s}{t}?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3w^2+11w-c=0\\
&\mathrm{In~the~given~equation,~}c\text{ is a constant. A solution to the given equation is }\frac{-11+\sqrt{433}}{6}.\\
&\text{What is the value of }c?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^2+49x+1=0\\&\text{What is one of the solutions to the given equation?}
\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x(x-18)=c\\
&\text{In the given equation, }c\text{ is a constant A solution to the equation is }k+7\sqrt{2}\mathrm{~where~}k\\&\text{is an integer. What is the value of }c?\end{aligned}\)

\(\mathrm{If~}(x+3)^2=30,\text{ what is the value of }x^2+6x?\)

\(\text{If }\left(\frac{1}{2}x-\frac{23}{2}\right)^2-81=0,\text{ what is the value of }(x-23)^2?\)

\(\text{If }\left(\frac{1}{2}x-\frac{33}{2}\right)^2-64=0,\text{ what is the value of }(x-33)^2?\)

\(\mathrm{If~}4x^{2}-24x-36=0,\text{ what is the value of }x^{2}-6x?\)

\(\mathrm{If~}4x^{2}-12x-24=0,\text{ what is the value of }x^{2}-3x?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\sqrt{\left(x-2\right)^{2}}=\sqrt{3x+34}\\&\text{What is the smallest solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{x+1}{5x^{2}}=\frac{k}{x}\\
&\text{In the given equation, }k\text{ is a constant. The solution to the given equation is }\frac{1}{174}.\\&\text{What is the value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~(2x-7)^2-8(2x-7)+15=0\\&\text{What is a solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&\text{Two numbers have a product }y\text{ such that one number }x\text{ and the other number}\\
&\text{is 99 less than }x.\text{Which of the following equations represents the relationship}\\&\text{between }y\text{ and }x?\end{aligned} \)

\(\begin{aligned}
&\text{The function }f\text{ gives the product of a number, }x\text{, and a number that is }\\&91\mathrm{~more~than~}x.\text{ Which equation defines }f?\end{aligned}\)

\(\begin{aligned}&\text{The product of a positive number }x\text{ and the number that is 5 more than }x\text{ is 104.}\\&\text{What is the value of }x?\\\end{aligned}\)

\(\begin{aligned}&\text{The product of a positive number }x\text{ and the number that is 1 less than }x\text{ is 342.}\\&\text{What is the value of }x?\\\end{aligned}\)

\(\begin{aligned}
&\text{The product of two positive integers is 546. If the first integer is 11 greater than twice the second}\\
&\mathrm{integer,~what~is~the~smaller~of~the~two~integers?}\end{aligned}\)

\(\begin{aligned}
&\text{A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the}\\
&\text{width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?}\end{aligned}\)

\(\begin{aligned}
&\text{A club plans to sell tote bags. The club members estimate they will sell 80 tote bags when the }\\
&\text{bags are priced at \$9 each. For every price increase of \$1, they estimate they will sell 8 fewer }\\
&\text{bags. What is the estimated revenue, in dollars, when the bags are priced at \$12 each?}\\&\text{(revenue = price}\times\text{number of bags sold})\end{aligned}\)

\(\begin{aligned}
&\text{A company developed a plan to set the selling price of a product. The company determined that for a}\\
&\text{selling price of \$120.00, zero products would be sold. For each \$1.50 decrease in the selling price, the}\\
&\text{number of products sold would increase by one. For a revenue of exactly \$1,966.50, which of the following}\\
&\text{could be the number of products sold? (revenue}=\mathrm{price}\times\text{number of products sold})\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^{2}-x-12=0\\&\text{What is the sum of the solutions to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3x^{2}-2x-7=0\\&\text{What is the sum of the solutions to the given equation?}\end{aligned}\)

\(\text{What is the sum of all values of }m\text{ that satisfy }2m^{2}-16m+8=0?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~x(x+1)-56=4x(x-7)\\&\text{What is the sum of the solutions to the given equation?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(x-42)^2=1\\
&\text{What is the sum of the solutions to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~x(x+4)-140=3x(x-10)\\&\text{What is the sum of the solutions to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~12(w-a)(w+8)=4(w+8)\\
&\text{In the given equation, }a\text{ is a constant. The sum of the solutions to the equation is }\frac{34}{3}.\\&\text{What is the value of }a?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~33x^2+(33s+r)x+rs=0\\
&\text{In the given equation, }r\text{ and }s\text{ are positive constants. The product of the solutions to the given}\\
&\text{equation is }krs,\mathrm{~where~}k\text{ is a constant. What is the value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~125x^2-(25a+5b)x+ab=\mathrm{0}\\
&\text{In the given equation, }a\mathrm{~and~}b\text{ are positive constants. The sum of the solutions to the given}\\
&\text{equation is }k(5a+b)\text{, where }k\text{ is a constant. What is the value of }k?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{1}{46}x^2+\left(s-\frac{1}{46}t\right)x-st=0\\
&\text{In the given equation, }s\text{ and }t\text{ are positive constants. The product of the solutions to the given}\\&\text{equation is }-2kst,\mathrm{~where~}k\text{ is a constant. What is the value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(x-k)^2=(k-4a)(x-k)\\
&\text{In the given equation, }a\text{ and }k\text{ are constants, where } k > 4a.\text{ The sum of the solutions to}\\
&\text{the equation is 3}k+35.\text{ What is the value of }a?\end{aligned}\)

\(\begin{aligned}
&\text{The solutions to }x^2+10x+23=0\text{ are }r\text{ and }s,\text{ where } r< s.\text{ The solutions}\\
&\text{to }x^{2}+10x+17=0{\mathrm{~are~}}t{\mathrm{~and~}}u,{\mathrm{~where~}} t < u.\text{ The solutions to }\\
&x^{2}+20x+c=0,\mathrm{where~}c\text{ is a constant, are }r+u\mathrm{~and~}s+t.\mathrm{~What~is~the}\\&\text{value of }c?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^2=2,601\\
&\text{How many distinct real solutions does this given equation have?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^2-100=0\\
&\text{How many distinct real solutions does this given equation have?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(x+81)^2=256\\
&\text{How many distinct real solutions does this given equation have?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(x+k)^2+31=31\\
&\text{In the given equation, }k\text{ is a constant. How many distinct real solutions does this equation have?}\end{aligned}\)

\(\begin{aligned}&\text{The quadratic equation }\left(2x-64\right)^2=a,\mathrm{~where~}a\text{ is a constant, has exactly one real}\\&\text{solution. What is the value of }a?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-(3x-7)^2=p+16\\
&\mathrm{In~the~equation,~}p\text{ is an integer constant. The equation has no real solution. What is the}\\&\text{least possible value of }p?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~5x^{2}+10x+16=0\\&\text{How many distinct real solutions does the given equation have?}\end{aligned}\\\)

\(\text{Which quadratic equation has no real solutions?}\)

\(\text{Which quadratic equation has exactly one distinct real solution?}\)

\(\text{Which quadratic equation has no real solution?}\)

\(\begin{aligned}
&\text{In the equation }10x^{2}+50x+c=0,~c\text{ is a constant. If the equation has exactly one solution,}\\&\text{what is the value of }c?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4x^{2}+kx+9=0\\
&\mathrm{In~the~given~equation,~}k\text{ is a positive constant. The equation has exactly one real solution.}\\&\text{What is the value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\sqrt{k-x}=52-x\\
&\mathrm{In~the~given~equation,~}k\text{ is a constant. The equation has exactly one real solution.}\\&\text{What is the minimum possible value of }4k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2x^{2}-4x=t\\
&\mathrm{In~the~equation~above,~}t\text{ is a constant. If the equation has no real solutions, }\\&\text{which of the following could be the value of }t?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^{2}-12x+c=0\\
&\mathrm{In~the~given~equation,~}c\mathrm{~is~a~constant.~The~equation~has~ no~ real~ solutions~ if~ } c > n. \\&\text{What is the least possible value of }n?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^{2}-34x+c=0\\
&\mathrm{In~the~given~equation,~}c\mathrm{~is~a~constant.~The~equation~has~ no~ real~ solutions~ if~ } c > n. \\&\text{What is the least possible value of }n?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4x^{2}+21=48x+r\\&\mathrm{In~the~given~equation,~}r\text{ is a constant. The equation has exactly one real solution.}\\&\text{What is the value of }r?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~9x^2+8=nx\\&\text{In the given equation, }n\text{ is a constant. The equation has exactly one solution. What is the}\\&\text{value of }\frac{n^2}{8}?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~nx^2-16x=26x^2-8\\&\text{In the given equation, }n\text{ is an integer constant. If the equation has two distinct real solutions,}\\&\text{what is the greatest possible value of }n?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^{2}+\left(\sqrt{k-3}\right)x+42=0\\&\text{In the given equation, }k\text{ is a constant. The equation has exactly one real solution. What is the}\\&\text{value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~88x^2+bx+c=0\\
&\text{In the given equation, }b\mathrm{~and~}c\text{ are positive constants. The equation has more than one real}\\
&\text{solution. Which of the following describes the relationship between }b\text{ and }c?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r^2+qr=2r-55\\
&\text{In the given equation, }q\text{ is an integer constant. The given equation has no real solutions. What is }\\&\text{the largest possible value of }q?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x(kx-56)=-16\\
&\mathrm{In~the~given~equation,~}k\text{ is an integer constant. If the equation has no real solution, what is }\\&\text{the least possible value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x(kx-40)=-8\\
&\mathrm{In~the~given~equation,~}k\text{ is an integer constant. If the equation has two distinct real solutions, }\\&\text{what is the greatest possible value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-x^{2}+bx-676=0\\
&\mathrm{In~the~given~equation,~}b\text{ is a positive integer. The equation has no real solution. What is }\\&\text{the greatest possible value of }b ?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{1}{cx}=\frac{x}{96}+\frac{1}{c}\\&\mathrm{In~the~given~equation,~}c\text{ is a constant. If the equation has exactly one solution, what is}\\&\text{the value of }c?\end{aligned}\)

\(\text{What is the }y\text{-intercept of the graph of }y=2x^2+6x+3 \text{ in the }xy\text{-plane?}\)

\(\text{The~}y\text{-intercept of the graph of }y=2x^2+27\text{ is }(0,y).\text{ What is the value of }y?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y=-\frac{1}{4}x^{2}+x+29\\
&\text{The given equation models a company’s active projects over 6 months, where }y\text{ is the estimated}\\
&\text{number of active projects }x\text{ months after the end of April 2013, where }0\leq x\leq6.\text{ Which }\\
&\text{statement is the best interpretationof the }y\text{-intercept of the graph of this equation in the}\\&xy\text{-plane?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=-16x^{2}+99\\
&\text{The function }f\text{ gives the estimated height, in feet, of an acorn }x\text{ seconds after the acorn}\\
&\text{fell from a tree. Based on the function, what is the estimated height, in feet, of an acorn}\\&\text{before it fell from the tree?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~h(t)=-16t^{2}+110t+72\\
&\text{The function above models the height }h\text{, in feet, of an object above ground }t\text{ seconds after }\\
&\text{being launched straight up in the air. What does the number 72 represent in the function?}
\end{aligned}\)

\(\begin{aligned}
&\text{An object is kicked from a platform. The equation }h=-4.9t^{2}+7t+9\text{ represents this situation,}\\
&\text{where }h\text{ is the height of the object above the ground, in meters, }t\text{ seconds after it is kicked. }\\
&\text{Which number represents the height, in meters, from which the object was kicked?}\end{aligned}\)

\(\begin{aligned}
&\text{A competitive diver dives from a platform into the water. The graph shown gives the height above }\\
&\mathrm{the~water~}y,\mathrm{~in~meters,~of~the~diver~}x\text{ seconds after diving from the platform. What is the best }\\
&\mathrm{interpretation~of~the~}x\text{-intercept of the graph?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~h(t)=-16t^{2}+b\\
&\text{The function }h\text{ estimates an object’s height, in feet above the ground }t\text{ seconds after the }\\
&\text{object is dropped, where }b\text{ is a constant. The function estimates that the object is 3,364 }\\
&\text{feet above the ground when it is dropped at }t=0.\text{ Approximately how many seconds }\\&\text{after being dropped does the function estimate the object will hit the ground?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=4x^{2}-50x+126\\
&\text{The given equation defines the function }f.\mathrm{~For~what}\text{value of }x\mathrm{~does~}f(x)\text{ reach }\\&\text{its minimum?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y=x^{2}-14x+22\\
&\text{The given equation relates the variables }x\text{ and }y.\text{ For what value of }x \text { does the value of }y\\&\text{reach its minimum?}\end{aligned}\)

\(\begin{aligned}
&\text{An auditorium has seats for 3,200 people. Tickets to attend a show at the auditorium currently cost \$8.00.}\\
&\text{For each \$1.00 increase to the ticket price, 100 fewer tickets will be sold. This situation can be modeled by}\\
&\text{the equation }y=-100x^{2}+2,400x+25,600,\mathrm{where~}x\text{ represents the increase in ticket price,
in dollars, and}\\
&y\text{ represents the revenue, in dollars, from ticket sales. If this equation is graphed in the }xy\text{-plane, at what}\\
&\text{value of }x\text{ is the maximum of the graph?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~p(x)=2x^2+20x+15\\&\text{What is the minimum value of the given function?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=4x^{2}+64x+262\\
&\text{The function }g\text{ is defined by }g(x)=f(x+5).\text{ For what value of }x\text{ does }g(x)\\
&\text{reach its minimum?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=5x^{2}+60x+181\\
&\text{The function }g\text{ is defined by }g(x)=f(x+8).\text{What is the minimum value of }g(x)?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=x^2-4x-320\\&\text{The function }f\text{ is defined by the given equation. Which of the following equivalent forms of}\\&\text{the equation displays the minimum value of the function as a constant or coefficient?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r(t)=55t-2t^2\\&\text{The function }r\text{ is defined by the given equation. The function }s\text{ is defined by}\\&s(t)=r(t)+1.\text{ Which expression represents the maximum value of }s(t)?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=(x-10)(x+13)\\
&\text{The function }f\text{ is defined by the given equation. For what value of }x\mathrm{~does~}f(x)\\&\mathrm{reach~its~minimum?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=(x-2)(x+15)\\
&\text{The function }f\text{ is defined by the given equation. For what value of }x\mathrm{~does~}f(x)\\&\mathrm{reach~its~minimum?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=(2x-20)(2x+8)\\&\text{What is the minimum value of the given function?}\end{aligned}\)

\(\begin{aligned}
&\mathrm{The~graph~of~the~quadratic~function~}y=f(x)\text{ in the }xy\text{-plane intersects the }x\text{-axis}\\
&\text{when }x=39\text{ and when }x=p,\mathrm{where~}p\text{ is a constant. The maximum value }y=f(x)\\&\text{occurs at the point }(14,m),\mathrm{~where~}m\text{ is a constant. What is the value of }p?\end{aligned}\)

\(\begin{aligned}
&\mathrm{Function~}f\text{ is a quadratic function where }f(-20)=0\text{ and }f(-4)=0.\text{ The graph of }y=f(x)\\&\text{in the }xy\text{-plane has a vertex at }(r,-64).\text{ What is the value of }r?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=-(x-6)^{2}+4\\&\text{The function }f\text{ is defined by the given equation. For what value of }x\mathrm{~does~}f(x)\mathrm{~reach}\\&\mathrm{its~maximum?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~g(x)=x^2+55\\&\text{What is the minimum value of the given function?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=(x-2)^2+9\\&\text{What is the minimum value of the given function?}\end{aligned}\)

\(\text{The graph of the quadratic function }y=f(x)\mathrm{~is}\text{ shown. What is the vertex of the graph?}\)

\(\begin{aligned}
&\text{An equation of the graph shown is }y=-\frac{1}{4}(x-p)^2+4,\mathrm{~where~}p\text{ is an integer constant.}\\&\text{What is the value of }p?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y=4x^2-bx-5\\
&\text{Which of the following equations is equivalent to the given equation, where }b\text{ is a positive }\\&\text{constant?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~m(t)=-0.0274\left(\frac{t}{7}\right)^{2}+7.3873\left(\frac{t}{7}\right)+75.032\\
&\text{The function }m\text{ gives the predicted body mass }m(t),\text{in kilograms (kg), of a certain animal }t\text{ days }\\
&\text{after it was born in a wildlife reserve, where }t\leq390.\text{ Which of the following is the best }\\&\text{interpretation of the statement “}m(330)\text{ is approximately equal to 362″ in this context}?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~h(t)=-4.9t^{2}+10t\\
&\text{The function }h\text{ models the height }h(t),\text{ in meters, of a football }t\text{ seconds after it is}\\
&\text{kicked. What is the interpretation of }h(2)=0.40\mathrm{~in~this~context?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=-8x^2+101x\\
&\text{The function }f\text{ models the depth below sea level, in meters, of a certain seal }x\mathrm{~minutes}\\
&\text{after the seal dives into the water. What is the best interpretation of }f(2)=170\mathrm{~in~this}\\&\mathrm{context?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=-0.0038400x^2+15.236x-15,103\\&\text{The model shown gives the predicted average Arctic sea ice area }f(x),\mathrm{in}\\&\text{millions of square kilometers, for September of each year }x,\mathrm{where~}x\\&\text{represens a year and 1979}\leq x\leq2012.\text{ Based on the model, what is the}\\&\text{positive difference, in millions of square kilometers, between the predicted}\\&\text{average Arctic sea ice area for September of the year 1991 and the predicted}\\&\text{average Arctic sea ice area for September of the year 1992? (Round your}\\&\text{answer to the nearest thousandth.}\end{aligned}\)

\(\begin{aligned}
&\text{The function }f(x)=\frac{1}{9}(x-7)^{2}+3\text{ gives a metal ball’s height above the ground }f(x),\\
&\text{in inches, }x\text{ seconds after it started moving on a track, where }0\leq x\leq10.\text{ Which of the }\\&\text{following is the best interpretation of the vertex of the graph of }y=f(x)\text{ in the }xy\text{-plane?}\end{aligned}\)

\(\begin{aligned}
&\text{The equation }y=-4.9(x-9.1)^{2}+10700\text{ give the estimated height above the ground, }y,\\
&\mathrm{in~meters,~of~a~plane,~were~}x\mathrm{~is}\text{ the number of seconds since it started a parabolic maneuver.}\\
&\text{If this equation is graphed in the }xy\text{-plane, which of the following is the best interpretation }\\&\text{of the vertex of the graph?}\end{aligned}\)

\(\begin{aligned}&\text{A machine launches a baseball from ground level. The baseball reaches a maximum }\\
&\text{height of 92.16 meters above the ground at 2.4 seconds and hits the ground at 4.8 }\\
&\text{seconds. Which equation represents the height above ground }h,\text{ in meters, of the }\\&\text{baseball }t\text{ seconds after it is launched?}\end{aligned}\)

\(\begin{aligned}&\text{An object is launched from a height of 121 feet above the ground. A quadratic function }f\\&\text{models the height above the ground, in feet, of the object }t\text{ seconds after it is launched.}\\&\text{According to the model, 2 seconds after the object is launched, it reaches a maximum height}\\&\text{of 185 feet above the ground. Which equation defines }f?\end{aligned}\)

\(\begin{aligned}
&\text{The function } g\text{ is a quadratic function . In the }xy\text{-plane, the graph of }y=g(x)\text{ has a}\\
&\mathrm{vertex~at~(-1,~-4)~and~passes~through~the~points~(-2,-43)~and~(1,-160).~What~is~}\\&\text{the value of }g(0)-g(2)?\end{aligned}\)

\(\begin{aligned}
&\mathrm{Function~}f\text{ is a quadratic function. The graph of }y=f(x)\text{ in the }xy\text{-plane~has~a~vertex}\\
&\mathrm{at~(-8,1),~contains~the~point~(-9,-1),}\text{ and has a }y\text{-intercept at }(0,a).\mathrm{~The~graph~of}\\
&\mathrm{}y=6\cdot f(x)\mathrm{~has~a~}y\text{-intercept at }(0,b).\text{ What is the positive difference between }a\mathrm{~and~b?}\end{aligned}\)

\(\begin{aligned}
&\mathrm{For~a~certain~type~of~rope,~the~equation~}y=900ax^{2},\mathrm{~where~}a\mathrm{~is~a~constant,~gives~the}\\
&\text{estimated breaking strength }y,\mathrm{~in~pounds},\text{of a rope with a circumference of }x\mathrm{~inches.}\\
&\text{Based on this equation, if a rope of this type }\mathrm{has~a~circumference~of~2.75~inches,~it~has}\\
&\text{an estimated breaking strength of 9,528.75 pounds.}\text{ What is the estimated breaking}\\&\mathrm{strength,~in~pounds,~of~a~rope~of~this~type}\text{ that has a circumference of 7.50 inches?}\end{aligned}\)

\(\begin{aligned}
&\text{The quadratic function }g\text{ models the depth, in meters, below the surface of the water of a seal }\\
&t\text{ minutes after the seal entered the water during a maximum depth of 302.4 meters 6 minutes }\\
&\text{after it entered the water and then reached the surface of the water 12 minutes after it entered }\\
&\text{the water. Based on the function, what was the estimated depth, to the nearest meter, of the}\\&\text{seal 10 minutes after it entered the water?}\end{aligned}\)

\(\begin{aligned}
&\text{A quadratic function models the height, in feet, of an object above the ground in terms of the time, }\\
&\mathrm{in~seconds,~after~the~object~was~launched.~According~to~the~model,~the~object~was~launched~from}\\
&\text{a height of 0 feet and reached its maximum height of 1,600 feet 10 seconds after it was launched.}\\
&\text{Based on the model, what was the height, in feet, of the}\text{ object 15 seconds after it was launched?}\end{aligned}\)

\(\begin{aligned}&\text{A quadratic function gives the estimated length of daylight }d(t),\text{ in hours, in a certain city }t\\
&\text{months after March 1, where }0\leq t\leq7.\text{ According to the function, the estimated length of}\\&\text{daylight is 12.66 hours 6 months after March 1, and the maximum estimated length of daylight is}\\&\text{13.91 hours 3.5 months after March 1. Based on this function, what is the estimated length of}\\&\text{daylight, in hours, on March 1?}\end{aligned}\)

\(\begin{aligned}&\text{A quadratic model gives the predicted instantaneous rate of change, in bacteria per hour, of}\\&\text{a bacteria population as a function of the population size. According to the model, the}\\&\text{predicted instantaneous rate of change is 0 bacteria per hour for a population size of 0, and}\\&\text{the maximum predicted instantaneous rate of change is 0.200 hacteria per hour for a}\\&\text{population size of 7,000. Based on this model, what is the predicted instantaneous rate of}\\&\text{change, in bacteria per hour, of the bacteria population for a population size of 700?}\end{aligned}\)

\(\begin{aligned}
&\text{In the }xy\text{-plane, a parabola has vertex }(9,-14)\text{ and intersects the }x\text{-axis at two points.}\\
&\text{If the equation of the parabola is written in the form }y=ax^{2}+bx+c,\text{where }a,b,\mathrm{and~}c\\&\mathrm{are~constants,~which~of~the}\text{ following could be the value of }a+b+c?\end{aligned}\)

\(\begin{aligned}
&\text{The function }f\text{ is defined by }f(x)=ax^{2}+bx+c,\mathrm{~where~}a,b,\mathrm{and~}c\text{ are constants. The }\\
&\text{graph of }y=f(x)\text{ in the }xy\text{-plane passes through the points }(7,0)\mathrm{~and~}(-3,0).\mathrm{~If~}a\text{ is an}\\
&\text{integer greater than 1, which of the following could be the value of }a+b?\end{aligned}\)

\(\begin{aligned}
&\text{The function }f\text{ is defined by }f(x)=ax^{2}+bx+c,\mathrm{~where~}a,b,\mathrm{and~}c\text{ are constants, and}\\
& 1 < a < 4.\text{ The graph of }y=f(x)\text{ in the }xy\text{-plane passes through the points }(12,0)\mathrm{~and~}\\
&(-4,0).\text{ If }a\text{ is an integer , what could be the value of }a+b?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=ax^2+2x+c\\&\text{In the given quadratic function, }a\mathrm{~and~}c\text{ are constants. The graph of }y=f\left(x\right)\text{in the }xy\text{-plane}\\&\text{is a parabola that opens upward and has a vertex at the point }(h,k),\mathrm{where~}h\mathrm{~and~}k\mathrm{~are}\\&\text{constants. If } k < 0 \mathrm{~and~}f\left(-5\right)=f\left(1\right),\text{which of the following must be true?}\\&~~~~~~~~~~\mathrm{I.~} c < 0 \\&~~~~~~~~~\mathrm{II.~}a\geq1\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=(x-a)(x-b)\\&\text{The function }f\text{ is defined by the given equation, where }a\mathrm{~and~}b\text{ are integer constants. If}\\
&f(32)>0,~f(35)<0,\mathrm{~and~}f(38)>0,\text{ which of the following could be the value of }a+b?\end{aligned}\)