Question 1

Give a definition or an example of the word or phrase. Parabola

Accepted Answer

The graph of a quadratic function, a U shaped curve.

Question 2

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation
-$x^{2}=6 x-8$

Accepted Answer

A)  $\{-8,-1\}$ 
B)  $\{4,2\}$ 
C)  $\{-4,-2\}$ 
D)  $\{1,8\}$ 
A)  $\{-8,-1\}$ 
B)  $\{4,2\}$ 
C)  $\{-4,-2\}$ 
D)  $\{1,8\}$ B

Question 3

A 33-inch-square TV is on sale at the local electronics store. If 33 inches is the measure of the diagonal of the screen, use the Pythagorean theorem to find the length of the side of the screen.

Accepted Answer

A)  $\frac{1089}{2}$ 
B)  $\sqrt{33}$ in. 
C)  $\frac{\sqrt{33}}{2}$ in. 
D)  $\frac{33 \sqrt{2}}{2}$ in. 
A)  $\frac{1089}{2}$ 
B)  $\sqrt{33}$ in. 
C)  $\frac{\sqrt{33}}{2}$ in. 
D)  $\frac{33 \sqrt{2}}{2}$ in. D

Question 4

Solve the equation by completing the square.
-$2 n^{2}=-12 n-5$

Accepted Answer

A)  $\left\{\frac{-6+\sqrt{46}}{2}, \frac{-6-\sqrt{46}}{2}\right\}$ 
B)  $\left\{\frac{-6+\sqrt{26}}{4}, \frac{-6-\sqrt{26}}{4}\right\}$ 
C)  $\left\{\frac{-6+\sqrt{26}}{2}, \frac{-6-\sqrt{26}}{2}\right\}$ 
D)  $\left\{\frac{-12+\sqrt{26}}{2}, \frac{-12-\sqrt{26}}{2}\right\}$ 
A)  $\left\{\frac{-6+\sqrt{46}}{2}, \frac{-6-\sqrt{46}}{2}\right\}$ 
B)  $\left\{\frac{-6+\sqrt{26}}{4}, \frac{-6-\sqrt{26}}{4}\right\}$ 
C)  $\left\{\frac{-6+\sqrt{26}}{2}, \frac{-6-\sqrt{26}}{2}\right\}$ 
D)  $\left\{\frac{-12+\sqrt{26}}{2}, \frac{-12-\sqrt{26}}{2}\right\}$

Question 5

Decide whether the statement is true or false. If it is false, tell why.
-If $k$ is a positive number, then the equation $-x^{2}=-100 k$ has no real solutions.

Accepted Answer

A)  True 
B)  False; the equation is equivalent to $x^{2}=100 k$, where $x^{2}$ and $100 k$ are positive, so it will have two real solutions 
C)  False; the equation is equivalent to $x^{2}=100 k$, where $x^{2}$ and $100 k$ are positive, so the equation will have one real number solution 
A)  True 
B)  False; the equation is equivalent to $x^{2}=100 k$, where $x^{2}$ and $100 k$ are positive, so it will have two real solutions 
C)  False; the equation is equivalent to $x^{2}=100 k$, where $x^{2}$ and $100 k$ are positive, so the equation will have one real number solution

Question 6

Choose the one alternative that best completes the statement or answers the question.
Solve the equation for the indicated variable. (Leave in your answer, when appropriate.)
-$M=\pi r^{2} h d$ for $r$

Accepted Answer

A)  $r=\frac{ \pm \sqrt{\mathrm{M} \pi \mathrm{hd}}}{\pi \mathrm{hd}}$ 
B)  $\mathrm{r}=\frac{ \pm \sqrt{\pi \mathrm{Mhd}}}{\mathrm{hd}}$ 
C)  $r=\frac{ \pm M \sqrt{\pi h d}}{\pi h d}$ 
D)  $r= \pm \sqrt{\pi \text { Mhd }}$ 
A)  $r=\frac{ \pm \sqrt{\mathrm{M} \pi \mathrm{hd}}}{\pi \mathrm{hd}}$ 
B)  $\mathrm{r}=\frac{ \pm \sqrt{\pi \mathrm{Mhd}}}{\mathrm{hd}}$ 
C)  $r=\frac{ \pm M \sqrt{\pi h d}}{\pi h d}$ 
D)  $r= \pm \sqrt{\pi \text { Mhd }}$

Question 7

What is the usual first step taken in solving the equation $3 x^{2}-2 x=8$ by completing the square?

Accepted Answer

Divide bot

Question 8

Use the square root property to solve the equation.
-$(\mathrm{p}-2)^{2}=13$

Accepted Answer

A)  $\{\sqrt{13}-2,-\sqrt{13-2}\}$ 
B)  $\{2+\sqrt{13}, 2-\sqrt{13}\}$ 
C)  $\{\sqrt{13}-\sqrt{-2}\}$ 
D)  $\{2+\sqrt{13}\}$ 
A)  $\{\sqrt{13}-2,-\sqrt{13-2}\}$ 
B)  $\{2+\sqrt{13}, 2-\sqrt{13}\}$ 
C)  $\{\sqrt{13}-\sqrt{-2}\}$ 
D)  $\{2+\sqrt{13}\}$

Question 9

Solve the problem. Round your answer to the nearest tenth, when appropriate.
-A grasshopper is perched on a reed 6 inches above the ground. It hops off the reed and lands on the ground about 10.4 inches away. During its hop, its height is given by the equation $h=-0.2 x^{2}+1.50 x+6$, where $x$ is the distance in inches from the base of the reed, and $h$ is in inches. How far was the grasshopper from the base of the reed when it was 3.25 inches above the ground?

Accepted Answer

A)  1.5 in. 
B)  9.0 in. 
C)  3.2 in. 
D)  10.4 in. 
A)  1.5 in. 
B)  9.0 in. 
C)  3.2 in. 
D)  10.4 in.

Question 10

The calculator graphs shows the $x$-values of the $x$-intercepts of the graph of the polynomial in the equation. Use the graphs to solve the equation.
-$4 \mathrm{x}^{2}-20 \mathrm{x}+21=0$

Accepted Answer

A)  $\{-3.5,-1.5\}$ 
B)  $\{-29,21\}$ 
C)  $\{1.5,3.5\}$ 
D)  $\{6,14\}$ 
A)  $\{-3.5,-1.5\}$ 
B)  $\{-29,21\}$ 
C)  $\{1.5,3.5\}$ 
D)  $\{6,14\}$

Question 11

A boy is standing on a flat field and tosses his ball toward a second boy standing at the other end of the field. The path of the ball is a parabola, and the equation of the path is $f(x)=-4 x^{2}+8 x$. Based on this information, answer the question.
-The axis of the parabola is horizontal.

Accepted Answer

A) True 
 B)False

Question 12

Use the quadratic formula to solve the equation.
-$x^{2}-\frac{1}{5} x=-\frac{7}{10}$

Accepted Answer

A)  $\left\{\frac{-1+\mathrm{i} \sqrt{69}}{10}, \frac{-1-\mathrm{i} \sqrt{69}}{10}\right\}$ 
B)  $\left\{0,-\frac{7}{2} \mathrm{i}\right\}$ 
C)  $\left\{\frac{1+\mathrm{i} \sqrt{69}}{10}, \frac{1-\mathrm{i} \sqrt{69}}{10}\right\}$ 
D)  $\left\{\frac{1}{5} \mathrm{i}, 0\right\}$ 
A)  $\left\{\frac{-1+\mathrm{i} \sqrt{69}}{10}, \frac{-1-\mathrm{i} \sqrt{69}}{10}\right\}$ 
B)  $\left\{0,-\frac{7}{2} \mathrm{i}\right\}$ 
C)  $\left\{\frac{1+\mathrm{i} \sqrt{69}}{10}, \frac{1-\mathrm{i} \sqrt{69}}{10}\right\}$ 
D)  $\left\{\frac{1}{5} \mathrm{i}, 0\right\}$

Question 13

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve.
-$w^{2}+3 w+5=0$

Accepted Answer

A)  Two nonreal complex solutions 
B)  Two rational solutions 
C)  One rational solution 
D)  Two irrational solutions 
A)  Two nonreal complex solutions 
B)  Two rational solutions 
C)  One rational solution 
D)  Two irrational solutions

Question 14

Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation. (All solutions are real numbers.)
-$3 x(x+5)=2$

Accepted Answer

A)  $\{1\}$ 
B)  $\left\{-\frac{3}{5}\right\}$ 
C)  $\left\{\frac{15+\sqrt{249}}{6}, \frac{15-\sqrt{249}}{6}\right\}$ 
D)  $\left\{\frac{-15+\sqrt{249}}{6}, \frac{-15-\sqrt{249}}{6}\right\}$ 
A)  $\{1\}$ 
B)  $\left\{-\frac{3}{5}\right\}$ 
C)  $\left\{\frac{15+\sqrt{249}}{6}, \frac{15-\sqrt{249}}{6}\right\}$ 
D)  $\left\{\frac{-15+\sqrt{249}}{6}, \frac{-15-\sqrt{249}}{6}\right\}$

Question 15

John owns a hot dog stand. He has found that his profit is given by the equation $P=-x^{2}+50 x+71$, where $\mathrm{x}$ is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Accepted Answer

A)  46 hot dogs 
B)  26 hot dogs 
C)  25 hot dogs 
D)  23 hot dogs 
A)  46 hot dogs 
B)  26 hot dogs 
C)  25 hot dogs 
D)  23 hot dogs

Question 16

Choose the one alternative that best completes the statement or answers the question.
Solve the equation for the indicated variable. (Leave in your answer, when appropriate.)
-$r=\sqrt{\frac{A}{2 \pi}}$ for $A$

Accepted Answer

A)  $\mathrm{A}=2 \pi \mathrm{r}$ 
B)  $A= \pm \sqrt{2 \pi r}$ 
C)  $\mathrm{A}=2 \pi \mathrm{r}^{2}$ 
D)  $\mathrm{A}= \pm 2 \pi \sqrt{\mathrm{r}}$ 
A)  $\mathrm{A}=2 \pi \mathrm{r}$ 
B)  $A= \pm \sqrt{2 \pi r}$ 
C)  $\mathrm{A}=2 \pi \mathrm{r}^{2}$ 
D)  $\mathrm{A}= \pm 2 \pi \sqrt{\mathrm{r}}$

Question 17

Solve the problem using Galileo's formula, $d=16 t^{2}$. Round your answer to the nearest tenth.
-Eric has a treehouse $27 \mathrm{ft}$ above the ground. How long would it take a water balloon dropped from the treehouse to fall to the ground?

Accepted Answer

A)  $5.2 \mathrm{sec}$ 
B)  $2.8 \mathrm{sec}$ 
C)  $1.3 \mathrm{sec}$ 
D)  $11,664 \mathrm{sec}$ 
A)  $5.2 \mathrm{sec}$ 
B)  $2.8 \mathrm{sec}$ 
C)  $1.3 \mathrm{sec}$ 
D)  $11,664 \mathrm{sec}$

Question 18

Solve the inequality, and graph the solution set.
-$v^{2}-5 v+6 \geq 0$

Accepted Answer

A)  $(-\infty, 2]$
  
B)  $[2,3]$
  
C)  $(-\infty, 2] \cup[3, \infty)$
  
D)  $[3, \infty)$
  
A)  $(-\infty, 2]$
  
B)  $[2,3]$
  
C)  $(-\infty, 2] \cup[3, \infty)$
  
D)  $[3, \infty)$

Question 19

Solve the inequality, and graph the solution set.
-$(x-2)(x+4)>0$

Accepted Answer

A)  (-4,2)
  
B)  $ (-4, \infty) $
  
C)  $ (-\infty,-2) \cup(4, \infty) $
  
D)  $ (-\infty,-4) \cup(2, \infty) $
  
A)  (-4,2)
  
B)  $ (-4, \infty) $
  
C)  $ (-\infty,-2) \cup(4, \infty) $
  
D)  $ (-\infty,-4) \cup(2, \infty) $

Question 20

Choose the one alternative that best completes the statement or answers the question.
Solve the equation for the indicated variable. (Leave in your answer, when appropriate.)
-$\mathrm{E}=m \mathrm{c}^{2}$ for $\mathrm{c}$

Accepted Answer

A)  $c= \pm \sqrt{E m}$ 
B)  $c=E m$ 
C)  $c=\frac{E}{m}$ 
D)  $c= \pm \frac{\sqrt{E m}}{m}$ 
A)  $c= \pm \sqrt{E m}$ 
B)  $c=E m$ 
C)  $c=\frac{E}{m}$ 
D)  $c= \pm \frac{\sqrt{E m}}{m}$

Give a definition or an example of the word or phrase. Parabola

Choose the one alternative that best completes the statement or answers the question. Use the zero factor property to solve the equation - $x^{2}=6 x-8$

A 33-inch-square TV is on sale at the local electronics store. If 33 inches is the measure of the diagonal of the screen, use the Pythagorean theorem to find the length of the side of the screen.

Solve the equation by completing the square. - $2 n^{2}=-12 n-5$

Decide whether the statement is true or false. If it is false, tell why. -If $k$ is a positive number, then the equation $-x^{2}=-100 k$ has no real solutions.

Choose the one alternative that best completes the statement or answers the question. Solve the equation for the indicated variable. (Leave in your answer, when appropriate.) - $M=\pi r^{2} h d$ for $r$

What is the usual first step taken in solving the equation $3 x^{2}-2 x=8$ by completing the square?

Use the square root property to solve the equation. - $(\mathrm{p}-2)^{2}=13$

A boy is standing on a flat field and tosses his ball toward a second boy standing at the other end of the field. The path of the ball is a parabola, and the equation of the path is $f(x)=-4 x^{2}+8 x$ . Based on this information, answer the question. -The axis of the parabola is horizontal.

Use the quadratic formula to solve the equation. - $x^{2}-\frac{1}{5} x=-\frac{7}{10}$

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve. - $w^{2}+3 w+5=0$

Choose the one alternative that best completes the statement or answers the question. Use the quadratic formula to solve the equation. (All solutions are real numbers.) - $3 x(x+5)=2$

John owns a hot dog stand. He has found that his profit is given by the equation $P=-x^{2}+50 x+71$ , where $\mathrm{x}$ is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Choose the one alternative that best completes the statement or answers the question. Solve the equation for the indicated variable. (Leave in your answer, when appropriate.) - $r=\sqrt{\frac{A}{2 \pi}}$ for $A$

Solve the problem using Galileo's formula, $d=16 t^{2}$ . Round your answer to the nearest tenth. -Eric has a treehouse $27 \mathrm{ft}$ above the ground. How long would it take a water balloon dropped from the treehouse to fall to the ground?

Solve the inequality, and graph the solution set. - $v^{2}-5 v+6 \geq 0$ $Solve the inequality, and graph the solution set. - v^{2}-5 v+6 \geq 0$

Solve the inequality, and graph the solution set. - $(x-2)(x+4)>0$

Choose the one alternative that best completes the statement or answers the question. Solve the equation for the indicated variable. (Leave in your answer, when appropriate.) - $\mathrm{E}=m \mathrm{c}^{2}$ for $\mathrm{c}$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 9: Quadratic Equations, Inequalities, and Functions

Give a definition or an example of the word or phrase. Parabola

Choose the one alternative that best completes the statement or answers the question. Use the zero factor property to solve the equation - x2=6x−8x^{2}=6 x-8x2=6x−8

A 33-inch-square TV is on sale at the local electronics store. If 33 inches is the measure of the diagonal of the screen, use the Pythagorean theorem to find the length of the side of the screen.

Solve the equation by completing the square. - 2n2=−12n−52 n^{2}=-12 n-52n2=−12n−5

Decide whether the statement is true or false. If it is false, tell why. -If kkk is a positive number, then the equation −x2=−100k-x^{2}=-100 k−x2=−100k has no real solutions.

Choose the one alternative that best completes the statement or answers the question. Solve the equation for the indicated variable. (Leave in your answer, when appropriate.) - M=πr2hdM=\pi r^{2} h dM=πr2hd for rrr

What is the usual first step taken in solving the equation 3x2−2x=83 x^{2}-2 x=83x2−2x=8 by completing the square?

Use the square root property to solve the equation. - (p−2)2=13(\mathrm{p}-2)^{2}=13(p−2)2=13

The calculator graphs shows the xxx -values of the xxx -intercepts of the graph of the polynomial in the equation. Use the graphs to solve the equation. - 4x2−20x+21=04 \mathrm{x}^{2}-20 \mathrm{x}+21=04x2−20x+21=0

Use the quadratic formula to solve the equation. - x2−15x=−710x^{2}-\frac{1}{5} x=-\frac{7}{10}x2−51​x=−107​

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve. - w2+3w+5=0w^{2}+3 w+5=0w2+3w+5=0

Choose the one alternative that best completes the statement or answers the question. Use the quadratic formula to solve the equation. (All solutions are real numbers.) - 3x(x+5)=23 x(x+5)=23x(x+5)=2

John owns a hot dog stand. He has found that his profit is given by the equation P=−x2+50x+71P=-x^{2}+50 x+71P=−x2+50x+71 , where x\mathrm{x}x is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Choose the one alternative that best completes the statement or answers the question. Solve the equation for the indicated variable. (Leave in your answer, when appropriate.) - r=A2πr=\sqrt{\frac{A}{2 \pi}}r=2πA​​ for AAA

Solve the problem using Galileo's formula, d=16t2d=16 t^{2}d=16t2 . Round your answer to the nearest tenth. -Eric has a treehouse 27ft27 \mathrm{ft}27ft above the ground. How long would it take a water balloon dropped from the treehouse to fall to the ground?

Solve the inequality, and graph the solution set. - v2−5v+6≥0v^{2}-5 v+6 \geq 0v2−5v+6≥0

Solve the inequality, and graph the solution set. - (x−2)(x+4)>0(x-2)(x+4)>0(x−2)(x+4)>0

Choose the one alternative that best completes the statement or answers the question. Solve the equation for the indicated variable. (Leave in your answer, when appropriate.) - E=mc2\mathrm{E}=m \mathrm{c}^{2}E=mc2 for c\mathrm{c}c

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Choose the one alternative that best completes the statement or answers the question. Use the zero factor property to solve the equation - $x^{2}=6 x-8$

Solve the equation by completing the square. - $2 n^{2}=-12 n-5$

Decide whether the statement is true or false. If it is false, tell why. -If $k$ is a positive number, then the equation $-x^{2}=-100 k$ has no real solutions.

Choose the one alternative that best completes the statement or answers the question. Solve the equation for the indicated variable. (Leave in your answer, when appropriate.) - $M=\pi r^{2} h d$ for $r$

What is the usual first step taken in solving the equation $3 x^{2}-2 x=8$ by completing the square?

Use the square root property to solve the equation. - $(\mathrm{p}-2)^{2}=13$

Use the quadratic formula to solve the equation. - $x^{2}-\frac{1}{5} x=-\frac{7}{10}$

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve. - $w^{2}+3 w+5=0$

Choose the one alternative that best completes the statement or answers the question. Use the quadratic formula to solve the equation. (All solutions are real numbers.) - $3 x(x+5)=2$

John owns a hot dog stand. He has found that his profit is given by the equation $P=-x^{2}+50 x+71$ , where $\mathrm{x}$ is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Choose the one alternative that best completes the statement or answers the question. Solve the equation for the indicated variable. (Leave in your answer, when appropriate.) - $r=\sqrt{\frac{A}{2 \pi}}$ for $A$

Solve the problem using Galileo's formula, $d=16 t^{2}$ . Round your answer to the nearest tenth. -Eric has a treehouse $27 \mathrm{ft}$ above the ground. How long would it take a water balloon dropped from the treehouse to fall to the ground?

Solve the inequality, and graph the solution set. - $v^{2}-5 v+6 \geq 0$ $Solve the inequality, and graph the solution set. - v^{2}-5 v+6 \geq 0$

Solve the inequality, and graph the solution set. - $(x-2)(x+4)>0$

Choose the one alternative that best completes the statement or answers the question. Solve the equation for the indicated variable. (Leave in your answer, when appropriate.) - $\mathrm{E}=m \mathrm{c}^{2}$ for $\mathrm{c}$