Question 1

Graph the parabola.
-$f(x)=-2 x^{2}-2 x+2$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 2

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it.
-$c^{2}-8 c+16=0$

Accepted Answer

A)  Cannot be solved by factoring 
B)  $(c-4)(c+4)=0$ 
C)  $(c-4)^{2}=0$ 
D)  $(c+4)^{2}=0$ 
A)  Cannot be solved by factoring 
B)  $(c-4)(c+4)=0$ 
C)  $(c-4)^{2}=0$ 
D)  $(c+4)^{2}=0$

Question 3

Choose the one alternative that best completes the statement or answers the question.
-Describe how the graph of $y=(x-6)^{2}$ is shifted compared to the graph of $y=x^{2}$.

Accepted Answer

A)  The parabola is shifted 6 units to the left. 
B)  The parabola is shifted 6 units up. 
C)  The parabola is shifted 6 units to the right. 
D)  The parabola is shifted 6 units down. 
A)  The parabola is shifted 6 units to the left. 
B)  The parabola is shifted 6 units up. 
C)  The parabola is shifted 6 units to the right. 
D)  The parabola is shifted 6 units down.

Question 4

Use the square root property to solve the equation.
-$8 z^{2}-200=0$

Accepted Answer

A)  $\{5\}$ 
B)  $\{6,-6\}$ 
C)  $\{5,-5\}$ 
D)  $\{102.5\}$ 
A)  $\{5\}$ 
B)  $\{6,-6\}$ 
C)  $\{5,-5\}$ 
D)  $\{102.5\}$

Question 5

Solve the problem. Round your answer to the nearest tenth, when appropriate.
-A rock falls from a tower that is 480 feet high. As it is falling, its height is given by the formula $\mathrm{h}=480-16 \mathrm{t}^{2}$. How many seconds will it take for the rock to hit the ground $(\mathrm{h}=0)$ ?

Accepted Answer

A)  $5.5 \mathrm{sec}$ 
B)  $21.5 \mathrm{sec}$ 
C)  $21.9 \mathrm{sec}$ 
D)  $14,400 \mathrm{sec}$ 
A)  $5.5 \mathrm{sec}$ 
B)  $21.5 \mathrm{sec}$ 
C)  $21.9 \mathrm{sec}$ 
D)  $14,400 \mathrm{sec}$

Question 6

Suppose that a problem asks you to find the height of a triangle, and that the problem leads to a quadratic equation. If $h$ represents the height of the triangle, which of the following solutions to the equation cannot be an answer to the problem?

Accepted Answer

A)  $\mathrm{h}=\frac{5}{4}$ 
B)  $h=1-\sqrt{5}$ 
C)  $\mathrm{h}=\frac{5}{2}$ 
D)  $h=1+\sqrt{5}$ 
A)  $\mathrm{h}=\frac{5}{4}$ 
B)  $h=1-\sqrt{5}$ 
C)  $\mathrm{h}=\frac{5}{2}$ 
D)  $h=1+\sqrt{5}$

Question 7

Solve by any method.
-$1-\frac{7}{x}-\frac{60}{x^{2}}=0$

Accepted Answer

A)  $\{-12,5\}$ 
B)  $\{12,5\}$ 
C)  $\{12,-5\}$ 
D)  $\{-12,-5\}$ 
A)  $\{-12,5\}$ 
B)  $\{12,5\}$ 
C)  $\{12,-5\}$ 
D)  $\{-12,-5\}$

Question 8

Find the vertex of the parabola
-$x=2 y^{2}-20 y+51$

Accepted Answer

A)  $(1,5)$ 
B)  $(5,0)$ 
C)  $(5,1)$ 
D)  $(0,1)$ 
A)  $(1,5)$ 
B)  $(5,0)$ 
C)  $(5,1)$ 
D)  $(0,1)$

Question 9

Use the discriminant of the equation to determine the number of $x$-intercepts.
-$f(x)=x^{2}+4 x+6$

Accepted Answer

A)  Two $x$-intercepts 
B)  One $x$-intercept 
C)  No x-intercepts 
A)  Two $x$-intercepts 
B)  One $x$-intercept 
C)  No x-intercepts

Question 10

Use the quadratic formula to solve the equation.
-$8 x^{2}-3 x+8=0$

Accepted Answer

A)  $\left\{\frac{3+\sqrt{247}}{16}, \frac{3-\sqrt{247}}{16}\right\}$ 
B)  $\left\{\frac{-3+\mathrm{i} \sqrt{247}}{16}, \frac{-3-\mathrm{i} \sqrt{247}}{16}\right\}$ 
C)  $\left\{\frac{-3+\sqrt{247}}{16}, \frac{-3-\sqrt{247}}{16}\right\}$ 
D)  $\left\{\frac{3+\mathrm{i} \sqrt{247}}{16}, \frac{3-\mathrm{i} \sqrt{247}}{16}\right\}$ 
A)  $\left\{\frac{3+\sqrt{247}}{16}, \frac{3-\sqrt{247}}{16}\right\}$ 
B)  $\left\{\frac{-3+\mathrm{i} \sqrt{247}}{16}, \frac{-3-\mathrm{i} \sqrt{247}}{16}\right\}$ 
C)  $\left\{\frac{-3+\sqrt{247}}{16}, \frac{-3-\sqrt{247}}{16}\right\}$ 
D)  $\left\{\frac{3+\mathrm{i} \sqrt{247}}{16}, \frac{3-\mathrm{i} \sqrt{247}}{16}\right\}$

Question 11

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.
-$4 x^{2}-19 x-5=0$

Accepted Answer

A)  $\{4,-5\}$ 
B)  $\{-0.25,5\}$ 
C)  $\{-5,0.25\}$ 
D)  $\{-1,20\}$ 
A)  $\{4,-5\}$ 
B)  $\{-0.25,5\}$ 
C)  $\{-5,0.25\}$ 
D)  $\{-1,20\}$

Question 12

Solve the equation.
-$\sqrt{\mathrm{x}}=20-\mathrm{x}$

Accepted Answer

A)  $\{9,-9\}$ 
B)  $\{-25,-16\}$ 
C)  $\{16\}$ 
D)  $\{\sqrt{20},-\sqrt{20}\}$ 
A)  $\{9,-9\}$ 
B)  $\{-25,-16\}$ 
C)  $\{16\}$ 
D)  $\{\sqrt{20},-\sqrt{20}\}$

Question 13

Find the value of $k$ so that the equation will have exactly one rational solution.
-$4 x^{2}+k x+4=0$

Accepted Answer

A)  -8 
B)  8 
C)  8 or -8 
D)  4 or -4 
A)  -8 
B)  8 
C)  8 or -8 
D)  4 or -4

Question 14

A rectangular garden has dimensions of 19 feet by 15 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 552 square feet?

Accepted Answer

A)  $8.5 \mathrm{ft}$ 
B)  $7 \mathrm{ft}$ 
C)  $8 \mathrm{ft}$ 
D)  $6 \mathrm{ft}$ 
A)  $8.5 \mathrm{ft}$ 
B)  $7 \mathrm{ft}$ 
C)  $8 \mathrm{ft}$ 
D)  $6 \mathrm{ft}$

Question 15

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.
-$-2 x^{2}-3 x+5=0$

Accepted Answer

A)  $\{-1,2.5\}$ 
B)  $\{-5,2\}$ 
C)  $\{-3,5\}$ 
D)  $\{-2.5,1\}$ 
A)  $\{-1,2.5\}$ 
B)  $\{-5,2\}$ 
C)  $\{-3,5\}$ 
D)  $\{-2.5,1\}$

Question 16

If an object is thrown upward with an initial velocity of $12 \mathrm{ft}$ per sec, then its height (in feet) is given by $h(t)=-12 t^{2}+48 t$ after time $t$ seconds. What is its maximum height?

Accepted Answer

A)  $24 \mathrm{ft}$ 
B)  $144 \mathrm{ft}$ 
C)  $48 \mathrm{ft}$ 
D)  $146 \mathrm{ft}$ 
A)  $24 \mathrm{ft}$ 
B)  $144 \mathrm{ft}$ 
C)  $48 \mathrm{ft}$ 
D)  $146 \mathrm{ft}$

Question 17

Use the discriminant of the equation to determine the number of $x$-intercepts.
-$f(x)=3 x^{2}-6 x+3$

Accepted Answer

A)  No $x$-intercepts 
B)  Two x-intercepts 
C)  One $x$-intercept 
A)  No $x$-intercepts 
B)  Two x-intercepts 
C)  One $x$-intercept

Question 18

Choose the one alternative that best completes the statement or answers the question.
Identify which graph matches the equation.
-$f(x)=-x^{2}+2$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Tell what restrictions, if any, must be made on $s, k$, and $w$ to guarantee that $d$ is a real number. Assume that $\mathrm{s}, \mathrm{k}$, and $\mathrm{w}$ are all real numbers and that the denominator is not zero.
$\mathrm{d}=\frac{\sqrt{\mathrm{skw}}}{\mathrm{kw}}$

Accepted Answer

Either all must be p

Question 20

What is the discriminant for $4 x^{2}-12 x+9=0$ ? How many and what type of solutions does this equation have?

Accepted Answer

A)  Discriminant: 64; Two rational solutions 
B)  Discriminant: 63; Two irrational solutions 
C)  Discriminant: 0; One rational solution 
D)  Discriminant: -64; Two nonreal complex solutions 
A)  Discriminant: 64; Two rational solutions 
B)  Discriminant: 63; Two irrational solutions 
C)  Discriminant: 0; One rational solution 
D)  Discriminant: -64; Two nonreal complex solutions

Graph the parabola. - $f(x)=-2 x^{2}-2 x+2$ $Graph the parabola. - f(x)=-2 x^{2}-2 x+2$

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - $c^{2}-8 c+16=0$

Choose the one alternative that best completes the statement or answers the question. -Describe how the graph of $y=(x-6)^{2}$ is shifted compared to the graph of $y=x^{2}$ .

Use the square root property to solve the equation. - $8 z^{2}-200=0$

Solve the problem. Round your answer to the nearest tenth, when appropriate. -A rock falls from a tower that is 480 feet high. As it is falling, its height is given by the formula $\mathrm{h}=480-16 \mathrm{t}^{2}$ . How many seconds will it take for the rock to hit the ground $(\mathrm{h}=0)$ ?

Suppose that a problem asks you to find the height of a triangle, and that the problem leads to a quadratic equation. If $h$ represents the height of the triangle, which of the following solutions to the equation cannot be an answer to the problem?

Solve by any method. - $1-\frac{7}{x}-\frac{60}{x^{2}}=0$

Find the vertex of the parabola - $x=2 y^{2}-20 y+51$

Use the discriminant of the equation to determine the number of $x$ -intercepts. - $f(x)=x^{2}+4 x+6$

Use the quadratic formula to solve the equation. - $8 x^{2}-3 x+8=0$

Solve the equation. - $\sqrt{\mathrm{x}}=20-\mathrm{x}$

Find the value of $k$ so that the equation will have exactly one rational solution. - $4 x^{2}+k x+4=0$

A rectangular garden has dimensions of 19 feet by 15 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 552 square feet?

If an object is thrown upward with an initial velocity of $12 \mathrm{ft}$ per sec, then its height (in feet) is given by $h(t)=-12 t^{2}+48 t$ after time $t$ seconds. What is its maximum height?

Use the discriminant of the equation to determine the number of $x$ -intercepts. - $f(x)=3 x^{2}-6 x+3$

Choose the one alternative that best completes the statement or answers the question. Identify which graph matches the equation. - $f(x)=-x^{2}+2$

Tell what restrictions, if any, must be made on $s, k$ , and $w$ to guarantee that $d$ is a real number. Assume that $\mathrm{s}, \mathrm{k}$ , and $\mathrm{w}$ are all real numbers and that the denominator is not zero. $\mathrm{d}=\frac{\sqrt{\mathrm{skw}}}{\mathrm{kw}}$

What is the discriminant for $4 x^{2}-12 x+9=0$ ? How many and what type of solutions does this equation have?

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

Graph the parabola. - f(x)=−2x2−2x+2f(x)=-2 x^{2}-2 x+2f(x)=−2x2−2x+2

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - c2−8c+16=0c^{2}-8 c+16=0c2−8c+16=0

Choose the one alternative that best completes the statement or answers the question. -Describe how the graph of y=(x−6)2y=(x-6)^{2}y=(x−6)2 is shifted compared to the graph of y=x2y=x^{2}y=x2 .

Use the square root property to solve the equation. - 8z2−200=08 z^{2}-200=08z2−200=0

Suppose that a problem asks you to find the height of a triangle, and that the problem leads to a quadratic equation. If hhh represents the height of the triangle, which of the following solutions to the equation cannot be an answer to the problem?

Solve by any method. - 1−7x−60x2=01-\frac{7}{x}-\frac{60}{x^{2}}=01−x7​−x260​=0

Find the vertex of the parabola - x=2y2−20y+51x=2 y^{2}-20 y+51x=2y2−20y+51

Use the discriminant of the equation to determine the number of xxx -intercepts. - f(x)=x2+4x+6f(x)=x^{2}+4 x+6f(x)=x2+4x+6

Use the quadratic formula to solve the equation. - 8x2−3x+8=08 x^{2}-3 x+8=08x2−3x+8=0

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. - 4x2−19x−5=04 x^{2}-19 x-5=04x2−19x−5=0

Solve the equation. - x=20−x\sqrt{\mathrm{x}}=20-\mathrm{x}x​=20−x

Find the value of kkk so that the equation will have exactly one rational solution. - 4x2+kx+4=04 x^{2}+k x+4=04x2+kx+4=0

A rectangular garden has dimensions of 19 feet by 15 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 552 square feet?

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. - −2x2−3x+5=0-2 x^{2}-3 x+5=0−2x2−3x+5=0

If an object is thrown upward with an initial velocity of 12ft12 \mathrm{ft}12ft per sec, then its height (in feet) is given by h(t)=−12t2+48th(t)=-12 t^{2}+48 th(t)=−12t2+48t after time ttt seconds. What is its maximum height?

Use the discriminant of the equation to determine the number of xxx -intercepts. - f(x)=3x2−6x+3f(x)=3 x^{2}-6 x+3f(x)=3x2−6x+3

Choose the one alternative that best completes the statement or answers the question. Identify which graph matches the equation. - f(x)=−x2+2f(x)=-x^{2}+2f(x)=−x2+2

Tell what restrictions, if any, must be made on s,ks, ks,k , and www to guarantee that ddd is a real number. Assume that s,k\mathrm{s}, \mathrm{k}s,k , and w\mathrm{w}w are all real numbers and that the denominator is not zero. d=skwkw\mathrm{d}=\frac{\sqrt{\mathrm{skw}}}{\mathrm{kw}}d=kwskw​​

What is the discriminant for 4x2−12x+9=04 x^{2}-12 x+9=04x2−12x+9=0 ? How many and what type of solutions does this equation have?

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

Graph the parabola. - $f(x)=-2 x^{2}-2 x+2$ $Graph the parabola. - f(x)=-2 x^{2}-2 x+2$

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - $c^{2}-8 c+16=0$

Choose the one alternative that best completes the statement or answers the question. -Describe how the graph of $y=(x-6)^{2}$ is shifted compared to the graph of $y=x^{2}$ .

Use the square root property to solve the equation. - $8 z^{2}-200=0$

Suppose that a problem asks you to find the height of a triangle, and that the problem leads to a quadratic equation. If $h$ represents the height of the triangle, which of the following solutions to the equation cannot be an answer to the problem?

Solve by any method. - $1-\frac{7}{x}-\frac{60}{x^{2}}=0$

Find the vertex of the parabola - $x=2 y^{2}-20 y+51$

Use the discriminant of the equation to determine the number of $x$ -intercepts. - $f(x)=x^{2}+4 x+6$

Use the quadratic formula to solve the equation. - $8 x^{2}-3 x+8=0$

Solve the equation. - $\sqrt{\mathrm{x}}=20-\mathrm{x}$

Find the value of $k$ so that the equation will have exactly one rational solution. - $4 x^{2}+k x+4=0$

If an object is thrown upward with an initial velocity of $12 \mathrm{ft}$ per sec, then its height (in feet) is given by $h(t)=-12 t^{2}+48 t$ after time $t$ seconds. What is its maximum height?

Use the discriminant of the equation to determine the number of $x$ -intercepts. - $f(x)=3 x^{2}-6 x+3$

Choose the one alternative that best completes the statement or answers the question. Identify which graph matches the equation. - $f(x)=-x^{2}+2$

Tell what restrictions, if any, must be made on $s, k$ , and $w$ to guarantee that $d$ is a real number. Assume that $\mathrm{s}, \mathrm{k}$ , and $\mathrm{w}$ are all real numbers and that the denominator is not zero. $\mathrm{d}=\frac{\sqrt{\mathrm{skw}}}{\mathrm{kw}}$

What is the discriminant for $4 x^{2}-12 x+9=0$ ? How many and what type of solutions does this equation have?