Question 1

Which one of the following methods cannot be used to solve the equation $x^{2}-4 x-8=0$ ?

Accepted Answer

A)  Completing the square 
B)  Quadratic formula 
C)  Factoring 
D)  All of the methods can be used. 
A)  Completing the square 
B)  Quadratic formula 
C)  Factoring 
D)  All of the methods can be used.

Question 2

Solve the inequality, and graph the solution set.
-$\frac{-6 x+2}{7 x^{2}+5}>0$

Accepted Answer

A)  $ \left(-\frac{1}{3}, \infty\right) $
  
B)  $ \left(-\infty,-\frac{3}{1}\right) $
  
C)  $ \left(-\infty, \frac{1}{3}\right) $
  
D)  $ (-\infty, 0) $
  
A)  $ \left(-\frac{1}{3}, \infty\right) $
  
B)  $ \left(-\infty,-\frac{3}{1}\right) $
  
C)  $ \left(-\infty, \frac{1}{3}\right) $
  
D)  $ (-\infty, 0) $

Question 3

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation
-$2 x^{2}-14 x+24=0$

Accepted Answer

A)  $\{3,4\}$ 
B)  $\{-3,4\}$ 
C)  $\{-4,3\}$ 
D)  $\{-4,-3\}$ 
A)  $\{3,4\}$ 
B)  $\{-3,4\}$ 
C)  $\{-4,3\}$ 
D)  $\{-4,-3\}$

Question 4

John owns a hot dog stand. His profit, in dollars, is given by the function $P(x)=-x^{2}+12 x+46$, where $\mathrm{x}$ is the number of hot dogs sold. What is the most he can earn?

Accepted Answer

A)  $\$ 130$ 
B)  $\$ 58$ 
C)  $\$ 36$ 
D)  $\$ 82$ 
A)  $\$ 130$ 
B)  $\$ 58$ 
C)  $\$ 36$ 
D)  $\$ 82$

Question 5

Solve the equation $y=4 x^{2}+b x-6$ for $x$. If $y$ is positive and $b$ is negative, what, if anything, can you determine about the signs of the solutions? Explain your reasoning.

Accepted Answer

@#LAT-DLM& or @#LAT-DLM&. Since @#LAT-DLM& is negative, the first term

Question 6

Identify the vertex of the given parabola.
-$f(x)=(x+5)^{2}+9$

Accepted Answer

A)  $(9,-5)$ 
B)  $(-5,9)$ 
C)  $(9,-25)$ 
D)  $(-9,5)$ 
A)  $(9,-5)$ 
B)  $(-5,9)$ 
C)  $(9,-25)$ 
D)  $(-9,5)$

Question 7

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.)
-$9 x^{2}+2 x-7=0$

Accepted Answer

A)  $\left\{\frac{9}{7}, 1\right\}$ 
B)  $\left\{\frac{9}{7},-1\right\}$ 
C)  $\left\{\frac{7}{9},-1\right\}$ 
D)  $\left\{\frac{9}{7}, 0\right\}$ 
A)  $\left\{\frac{9}{7}, 1\right\}$ 
B)  $\left\{\frac{9}{7},-1\right\}$ 
C)  $\left\{\frac{7}{9},-1\right\}$ 
D)  $\left\{\frac{9}{7}, 0\right\}$

Question 8

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.
-$6+5 z^{2}=-7 z$

Accepted Answer

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

Question 9

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.)
-$4 \pi r^{2}=A$ for $r$

Accepted Answer

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

Question 10

Solve the inequality, and graph the solution set.
-$x^{2}+3 x \geq-2$

Accepted Answer

A)  $(-\infty,-2]$
  
B)  $[-1, \infty)$
  
C)  $(-\infty,-2] \cup[-1, \infty)$
  
D)  $[-2,-1]$
  
A)  $(-\infty,-2]$
  
B)  $[-1, \infty)$
  
C)  $(-\infty,-2] \cup[-1, \infty)$
  
D)  $[-2,-1]$

Question 11

Identify the vertex of the given parabola.
-$f(x)=-6 x^{2}$

Accepted Answer

A)  $(0,-6)$ 
B)  $(6,0)$ 
C)  $(0,0)$ 
D)  $(-6,0)$ 
A)  $(0,-6)$ 
B)  $(6,0)$ 
C)  $(0,0)$ 
D)  $(-6,0)$

Question 12

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.
-$-x^{2}+4 x+5=0$

Accepted Answer

A)  $\{-5,1\}$ 
B)  $\{-5,-1\}$ 
C)  $\{-1,5\}$ 
D)  $\{4,5\}$ 
A)  $\{-5,1\}$ 
B)  $\{-5,-1\}$ 
C)  $\{-1,5\}$ 
D)  $\{4,5\}$

Question 13

Solve the equation by using the square root property or completing the square.
-$\mathrm{y}^{2}=12$

Accepted Answer

A)  $\{144\}$ 
B)  $\{6\}$ 
C)  $\{2 \sqrt{3},-2 \sqrt{3}\}$ 
D)  $\{\sqrt{12}\}$ 
A)  $\{144\}$ 
B)  $\{6\}$ 
C)  $\{2 \sqrt{3},-2 \sqrt{3}\}$ 
D)  $\{\sqrt{12}\}$

Question 14

Solve for $x$. Assume that $a$ and $b$ represent positive real numbers.
-$x^{2}=121 b$

Accepted Answer

A)  $\{-11 b, 11 b\}$ 
B)  $\{\sqrt{11 b},-\sqrt{11 b}\}$ 
C)  $\{-11 \mathrm{i} \sqrt{\mathrm{b}}, 11 \mathrm{i} \sqrt{\mathrm{b}}\}$ 
D)  $\{-11 \sqrt{b}, 11 \sqrt{b}\}$ 
A)  $\{-11 b, 11 b\}$ 
B)  $\{\sqrt{11 b},-\sqrt{11 b}\}$ 
C)  $\{-11 \mathrm{i} \sqrt{\mathrm{b}}, 11 \mathrm{i} \sqrt{\mathrm{b}}\}$ 
D)  $\{-11 \sqrt{b}, 11 \sqrt{b}\}$

Question 15

Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate.
-The length of a rectangle is $4 \mathrm{in}$. more than its width. If $2 \mathrm{in}$. are taken from the length and added to the width, the figure becomes a square with an area of $192 \mathrm{in.}^{2}$. What are the dimensions of the original figure?

Accepted Answer

A)  $11.9 \mathrm{in}$. by $15.9 \mathrm{in}$. 
B)  12.9 in. by $16.9 \mathrm{in}$. 
C)  10.9 in. by 14.9 in. 
D)  Cannot be determined without additional information 
A)  $11.9 \mathrm{in}$. by $15.9 \mathrm{in}$. 
B)  12.9 in. by $16.9 \mathrm{in}$. 
C)  10.9 in. by 14.9 in. 
D)  Cannot be determined without additional information

Question 16

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.)
-$(2 x-1)(x+1)=6$

Accepted Answer

A)  $\left\{\frac{1+\sqrt{57}}{4}, \frac{1-\sqrt{57}}{4}\right\}$ 
B)  $\left\{\frac{1+\sqrt{57}}{2}, \frac{1-\sqrt{57}}{2}\right\}$ 
C)  $\left\{\frac{-1+\sqrt{57}}{4}, \frac{-1-\sqrt{57}}{4}\right\}$ 
D)  $\left\{\frac{-1+\sqrt{37}}{2}, \frac{-1-\sqrt{37}}{2}\right\}$ 
A)  $\left\{\frac{1+\sqrt{57}}{4}, \frac{1-\sqrt{57}}{4}\right\}$ 
B)  $\left\{\frac{1+\sqrt{57}}{2}, \frac{1-\sqrt{57}}{2}\right\}$ 
C)  $\left\{\frac{-1+\sqrt{57}}{4}, \frac{-1-\sqrt{57}}{4}\right\}$ 
D)  $\left\{\frac{-1+\sqrt{37}}{2}, \frac{-1-\sqrt{37}}{2}\right\}$

Question 17

Find the vertex of the parabola
-$x=y^{2}+10 y+18$

Accepted Answer

A)  $(-5,-7)$ 
B)  $(-5,0)$ 
C)  $(0,-7)$ 
D)  $(-7,-5)$ 
A)  $(-5,-7)$ 
B)  $(-5,0)$ 
C)  $(0,-7)$ 
D)  $(-7,-5)$

Question 18

Solve the equation by completing the square.
-$\mathrm{z}^{2}+16 \mathrm{z}+52=0$

Accepted Answer

A)  $\{8+2 \sqrt{3}\}$ 
B)  $\{8+2 \sqrt{13}, 8-2 \sqrt{13}\}$ 
C)  $\{-8+2 \sqrt{3},-8-2 \sqrt{3}\}$ 
D)  $\{-16+2 \sqrt{13}\}$ 
A)  $\{8+2 \sqrt{3}\}$ 
B)  $\{8+2 \sqrt{13}, 8-2 \sqrt{13}\}$ 
C)  $\{-8+2 \sqrt{3},-8-2 \sqrt{3}\}$ 
D)  $\{-16+2 \sqrt{13}\}$

Question 19

Find the vertex of the parabola
-$f(x)=x^{2}-3$

Accepted Answer

A)  $(0,3)$ 
B)  $(3,0)$ 
C)  $(-3,0)$ 
D)  $(0,-3)$ 
A)  $(0,3)$ 
B)  $(3,0)$ 
C)  $(-3,0)$ 
D)  $(0,-3)$

Question 20

$2+\frac{5}{4 z-1}=\frac{-2}{(4 z-1)^{2}}$

Accepted Answer

A)  $\left\{-\frac{1}{4},-\frac{1}{8}\right\}$ 
B)  $\left\{-\frac{1}{4}, \frac{1}{8}\right\}$ 
C)  $\left\{-2,-\frac{1}{2}\right\}$ 
D)  $\left\{-\frac{1}{4}, 0\right\}$ 
A)  $\left\{-\frac{1}{4},-\frac{1}{8}\right\}$ 
B)  $\left\{-\frac{1}{4}, \frac{1}{8}\right\}$ 
C)  $\left\{-2,-\frac{1}{2}\right\}$ 
D)  $\left\{-\frac{1}{4}, 0\right\}$

Which one of the following methods cannot be used to solve the equation $x^{2}-4 x-8=0$ ?

Solve the inequality, and graph the solution set. - $\frac{-6 x+2}{7 x^{2}+5}>0$ $Solve the inequality, and graph the solution set. - \frac{-6 x+2}{7 x^{2}+5}>0$

Choose the one alternative that best completes the statement or answers the question. Use the zero factor property to solve the equation - $2 x^{2}-14 x+24=0$

John owns a hot dog stand. His profit, in dollars, is given by the function $P(x)=-x^{2}+12 x+46$ , where $\mathrm{x}$ is the number of hot dogs sold. What is the most he can earn?

Solve the equation $y=4 x^{2}+b x-6$ for $x$ . If $y$ is positive and $b$ is negative, what, if anything, can you determine about the signs of the solutions? Explain your reasoning.

Identify the vertex of the given parabola. - $f(x)=(x+5)^{2}+9$

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.) - $9 x^{2}+2 x-7=0$

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. - $6+5 z^{2}=-7 z$

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.) - $4 \pi r^{2}=A$ for $r$

Solve the inequality, and graph the solution set. - $x^{2}+3 x \geq-2$ $Solve the inequality, and graph the solution set. - x^{2}+3 x \geq-2$

Identify the vertex of the given parabola. - $f(x)=-6 x^{2}$

Solve the equation by using the square root property or completing the square. - $\mathrm{y}^{2}=12$

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers. - $x^{2}=121 b$

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.) - $(2 x-1)(x+1)=6$

Find the vertex of the parabola - $x=y^{2}+10 y+18$

Solve the equation by completing the square. - $\mathrm{z}^{2}+16 \mathrm{z}+52=0$

Find the vertex of the parabola - $f(x)=x^{2}-3$

$2+\frac{5}{4 z-1}=\frac{-2}{(4 z-1)^{2}}$

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

Which one of the following methods cannot be used to solve the equation x2−4x−8=0x^{2}-4 x-8=0x2−4x−8=0 ?

Solve the inequality, and graph the solution set. - −6x+27x2+5>0\frac{-6 x+2}{7 x^{2}+5}>07x2+5−6x+2​>0

Choose the one alternative that best completes the statement or answers the question. Use the zero factor property to solve the equation - 2x2−14x+24=02 x^{2}-14 x+24=02x2−14x+24=0

John owns a hot dog stand. His profit, in dollars, is given by the function P(x)=−x2+12x+46P(x)=-x^{2}+12 x+46P(x)=−x2+12x+46 , where x\mathrm{x}x is the number of hot dogs sold. What is the most he can earn?

Solve the equation y=4x2+bx−6y=4 x^{2}+b x-6y=4x2+bx−6 for xxx . If yyy is positive and bbb is negative, what, if anything, can you determine about the signs of the solutions? Explain your reasoning.

Identify the vertex of the given parabola. - f(x)=(x+5)2+9f(x)=(x+5)^{2}+9f(x)=(x+5)2+9

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.) - 9x2+2x−7=09 x^{2}+2 x-7=09x2+2x−7=0

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. - 6+5z2=−7z6+5 z^{2}=-7 z6+5z2=−7z

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.) - 4πr2=A4 \pi r^{2}=A4πr2=A for rrr

Solve the inequality, and graph the solution set. - x2+3x≥−2x^{2}+3 x \geq-2x2+3x≥−2

Identify the vertex of the given parabola. - f(x)=−6x2f(x)=-6 x^{2}f(x)=−6x2

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. - −x2+4x+5=0-x^{2}+4 x+5=0−x2+4x+5=0

Solve the equation by using the square root property or completing the square. - y2=12\mathrm{y}^{2}=12y2=12

Solve for xxx . Assume that aaa and bbb represent positive real numbers. - x2=121bx^{2}=121 bx2=121b

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.) - (2x−1)(x+1)=6(2 x-1)(x+1)=6(2x−1)(x+1)=6

Find the vertex of the parabola - x=y2+10y+18x=y^{2}+10 y+18x=y2+10y+18

Solve the equation by completing the square. - z2+16z+52=0\mathrm{z}^{2}+16 \mathrm{z}+52=0z2+16z+52=0

Find the vertex of the parabola - f(x)=x2−3f(x)=x^{2}-3f(x)=x2−3

2+54z−1=−2(4z−1)22+\frac{5}{4 z-1}=\frac{-2}{(4 z-1)^{2}}2+4z−15​=(4z−1)2−2​

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

Which one of the following methods cannot be used to solve the equation $x^{2}-4 x-8=0$ ?

Solve the inequality, and graph the solution set. - $\frac{-6 x+2}{7 x^{2}+5}>0$ $Solve the inequality, and graph the solution set. - \frac{-6 x+2}{7 x^{2}+5}>0$

Choose the one alternative that best completes the statement or answers the question. Use the zero factor property to solve the equation - $2 x^{2}-14 x+24=0$

John owns a hot dog stand. His profit, in dollars, is given by the function $P(x)=-x^{2}+12 x+46$ , where $\mathrm{x}$ is the number of hot dogs sold. What is the most he can earn?

Solve the equation $y=4 x^{2}+b x-6$ for $x$ . If $y$ is positive and $b$ is negative, what, if anything, can you determine about the signs of the solutions? Explain your reasoning.

Identify the vertex of the given parabola. - $f(x)=(x+5)^{2}+9$

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.) - $9 x^{2}+2 x-7=0$

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. - $6+5 z^{2}=-7 z$

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.) - $4 \pi r^{2}=A$ for $r$

Solve the inequality, and graph the solution set. - $x^{2}+3 x \geq-2$ $Solve the inequality, and graph the solution set. - x^{2}+3 x \geq-2$

Identify the vertex of the given parabola. - $f(x)=-6 x^{2}$

Solve the equation by using the square root property or completing the square. - $\mathrm{y}^{2}=12$

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers. - $x^{2}=121 b$

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.) - $(2 x-1)(x+1)=6$

Find the vertex of the parabola - $x=y^{2}+10 y+18$

Solve the equation by completing the square. - $\mathrm{z}^{2}+16 \mathrm{z}+52=0$

Find the vertex of the parabola - $f(x)=x^{2}-3$

$2+\frac{5}{4 z-1}=\frac{-2}{(4 z-1)^{2}}$