Question 1

Solve the equation by completing the square.
-$0.7 \mathrm{~m}^{2}+0.8 \mathrm{~m}+0.2=0$

Accepted Answer

A)  $\left\{\frac{-4+\sqrt{2}}{14}, \frac{-4-\sqrt{2}}{14}\right\}$ 
B)  $\left\{\frac{-4+\sqrt{2}}{7}, \frac{-4-\sqrt{2}}{7}\right\}$ 
C)  $\left\{\frac{-4+\sqrt{30}}{7}, \frac{-4-\sqrt{30}}{7}\right\}$ 
D)  $\left\{\frac{-8+\sqrt{2}}{7}, \frac{-8-\sqrt{2}}{7}\right\}$ 
A)  $\left\{\frac{-4+\sqrt{2}}{14}, \frac{-4-\sqrt{2}}{14}\right\}$ 
B)  $\left\{\frac{-4+\sqrt{2}}{7}, \frac{-4-\sqrt{2}}{7}\right\}$ 
C)  $\left\{\frac{-4+\sqrt{30}}{7}, \frac{-4-\sqrt{30}}{7}\right\}$ 
D)  $\left\{\frac{-8+\sqrt{2}}{7}, \frac{-8-\sqrt{2}}{7}\right\}$

Question 2

Solve the equation.
-$4 y=\sqrt{1-6 y}$

Accepted Answer

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

Question 3

Graph the parabola.
-$x=y^{2}+3$

Accepted Answer

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

Question 4

True or false? The equation $-x^{2}=-36$ has no real solutions. If false, give the solution or solutions.

Accepted Answer

A)  True 
B)  False; 6 and -6 
C)  False; 6 
D)  False; -6 
A)  True 
B)  False; 6 and -6 
C)  False; 6 
D)  False; -6

Question 5

Solve the inequality, and graph the solution set.
-$\frac{3 y+5}{y-4} \leq 0$

Accepted Answer

A)  $ \left[-\frac{5}{3}, 4\right) $
  
B)  $ \left[-\infty,-\frac{5}{3}\right] \cup[4, \infty) $
  
C)  $ \left[-\frac{5}{3}, 4\right] $
  
D)  $ \left[-\infty,-\frac{5}{3}\right] \cup(4, \infty) $
  
A)  $ \left[-\frac{5}{3}, 4\right) $
  
B)  $ \left[-\infty,-\frac{5}{3}\right] \cup[4, \infty) $
  
C)  $ \left[-\frac{5}{3}, 4\right] $
  
D)  $ \left[-\infty,-\frac{5}{3}\right] \cup(4, \infty) $

Question 6

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.
-How many $x$-intercepts are there on the graph of the equation?

Accepted Answer

A)  1 
B)  2 
C)  0 
D)  None of the above 
A)  1 
B)  2 
C)  0 
D)  None of the above

Question 7

Solve the equation by completing the square.
-$4 m^{2}+15 m=0$

Accepted Answer

A)  $\{0\}$ 
B)  $\left\{\frac{15}{4},-\frac{15}{4}\right\}$ 
C)  $\left\{-\frac{15}{4}, 0\right\}$ 
D)  $\left\{\frac{15}{4}, 0\right\}$ 
A)  $\{0\}$ 
B)  $\left\{\frac{15}{4},-\frac{15}{4}\right\}$ 
C)  $\left\{-\frac{15}{4}, 0\right\}$ 
D)  $\left\{\frac{15}{4}, 0\right\}$

Question 8

Describe how the graph of $y=x^{2}-4$ differs from the graph of $y=x^{2}$.

Accepted Answer

The graph

Question 9

$x=y^{2}-9 y+3$

Accepted Answer

A)  To the right; wider 
B)  To the right; narrower 
C)  To the left; same 
D)  To the right; same 
A)  To the right; wider 
B)  To the right; narrower 
C)  To the left; same 
D)  To the right; same

Question 10

Solve for $x$. Assume that $a$ and $b$ represent positive real numbers.
-$(3 x-4 b)^{2}=7 a$

Accepted Answer

A)  $\left\{\frac{\sqrt{16 b^{2}+7 a}}{9}, \frac{-\sqrt{16 b^{2}-7 a}}{9}\right\}$ 
B)  $\left\{\frac{4 b+\sqrt{7 a}}{3}, \frac{4 b-\sqrt{7 a}}{3}\right\}$ 
C)  $\left\{\frac{4 b+\sqrt{7 a}}{3} \cdot \frac{-\sqrt{4 b-7 a}}{3}\right\}$ 
D)  $\left\{\frac{4 b+7 a}{3}, \frac{-4 b-7 a}{3}\right\}$ 
A)  $\left\{\frac{\sqrt{16 b^{2}+7 a}}{9}, \frac{-\sqrt{16 b^{2}-7 a}}{9}\right\}$ 
B)  $\left\{\frac{4 b+\sqrt{7 a}}{3}, \frac{4 b-\sqrt{7 a}}{3}\right\}$ 
C)  $\left\{\frac{4 b+\sqrt{7 a}}{3} \cdot \frac{-\sqrt{4 b-7 a}}{3}\right\}$ 
D)  $\left\{\frac{4 b+7 a}{3}, \frac{-4 b-7 a}{3}\right\}$

Question 11

A projectile is thrown upward so that its distance above the ground after $t$ sec is given by $h(t)=-13 t^{2}+390 t$. After how many seconds does it reach its maximum height?

Accepted Answer

A)  $7 \mathrm{sec}$ 
B)  $15 \mathrm{sec}$ 
C)  $30 \mathrm{sec}$ 
D)  $22.5 \mathrm{sec}$ 
A)  $7 \mathrm{sec}$ 
B)  $15 \mathrm{sec}$ 
C)  $30 \mathrm{sec}$ 
D)  $22.5 \mathrm{sec}$

Question 12

Choose the equation that matches the graph.
-

Accepted Answer

A)  $x=(y+3)^{2}$ 
B)  $f(x)=(x+3)^{2}$ 
C)  $x=(y-3)^{2}$ 
D)  $f(x)=(x-3)^{2}$ 
A)  $x=(y+3)^{2}$ 
B)  $f(x)=(x+3)^{2}$ 
C)  $x=(y-3)^{2}$ 
D)  $f(x)=(x-3)^{2}$

Question 13

Sketch the graph of the parabola.
-

Accepted Answer

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

Question 14

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.
-$x^{2}-x-6=0$

Accepted Answer

A)  $\{-3,-2\}$ 
B)  $\{-3,2\}$ 
C)  $\{-2,3\}$ 
D)  $\{-1,-6\}$ 
A)  $\{-3,-2\}$ 
B)  $\{-3,2\}$ 
C)  $\{-2,3\}$ 
D)  $\{-1,-6\}$

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.
-$x^{2}+3 x-18=0$

Accepted Answer

A)  $\{-6,3\}$ 
B)  $\{-3,6\}$ 
C)  $\{-3,18\}$ 
D)  $\{0\}$ 
A)  $\{-6,3\}$ 
B)  $\{-3,6\}$ 
C)  $\{-3,18\}$ 
D)  $\{0\}$

Question 16

Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not actually solve.
-$w^{2}-10 w-6=0$

Accepted Answer

A)  9 
B)  25 
C)  -5 
D)  0 
A)  9 
B)  25 
C)  -5 
D)  0

Question 17

For the quadratic function, tell whether the graph opens up or down and whether the graph is wider, narrower, or the same shape as the graph of $f(x)=x^{2}$.
-$f(x)=\frac{1}{8} x^{2}-9$

Accepted Answer

A)  Up; narrower 
B)  Down; narrower 
C)  Down; wider 
D)  Up; wider 
A)  Up; narrower 
B)  Down; narrower 
C)  Down; wider 
D)  Up; wider

Question 18

Find the vertex of the parabola
-$f(x)=3 x^{2}-60 x+301$

Accepted Answer

A)  $(10,0)$ 
B)  $(1,0)$ 
C)  $(10,1)$ 
D)  $(1,10)$ 
A)  $(10,0)$ 
B)  $(1,0)$ 
C)  $(10,1)$ 
D)  $(1,10)$

Question 19

Find the mistake, then find the correct answer.
line $1 \quad x^{2}-6 x=-8$
line $2 \quad x^{2}-6 x+9=-8+9$
line $3 \quad(x-3)^{2}=1$
line $4 \quad x-3=\sqrt{1}$
line $5 \quad x-3=1$
line $6 \quad x-3+3=1+3$
line $7 \quad x=4$
line $8 \quad$ The solution set is $\{4\}$.

Accepted Answer

line 4 should be: @#LAT-DLM& or @#LAT-DLM&
line 5

Question 20

Find the mistake, then find the correct answer.
Solve for $\mathrm{x}: \mathrm{x}^{2}=50$
line $1 \quad \sqrt{x^{2}}=\sqrt{50}$
line $2 \quad x=2 \sqrt{5}$ or $x=-2 \sqrt{5}$
line 3 The solution set is $\{2 \sqrt{5},-2 \sqrt{5}\}$.

Accepted Answer

Line 2 reversed the

Solve the equation by completing the square. - $0.7 \mathrm{~m}^{2}+0.8 \mathrm{~m}+0.2=0$

Solve the equation. - $4 y=\sqrt{1-6 y}$

Graph the parabola. - $x=y^{2}+3$ $Graph the parabola. - x=y^{2}+3$

True or false? The equation $-x^{2}=-36$ has no real solutions. If false, give the solution or solutions.

Solve the inequality, and graph the solution set. - $\frac{3 y+5}{y-4} \leq 0$ $Solve the inequality, and graph the solution set. - \frac{3 y+5}{y-4} \leq 0$

Solve the equation by completing the square. - $4 m^{2}+15 m=0$

Describe how the graph of $y=x^{2}-4$ differs from the graph of $y=x^{2}$ .

$x=y^{2}-9 y+3$

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers. - $(3 x-4 b)^{2}=7 a$

A projectile is thrown upward so that its distance above the ground after $t$ sec is given by $h(t)=-13 t^{2}+390 t$ . After how many seconds does it reach its maximum height?

Choose the equation that matches the graph. -

Sketch the graph of the parabola. -

Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not actually solve. - $w^{2}-10 w-6=0$

For the quadratic function, tell whether the graph opens up or down and whether the graph is wider, narrower, or the same shape as the graph of $f(x)=x^{2}$ . - $f(x)=\frac{1}{8} x^{2}-9$

Find the vertex of the parabola - $f(x)=3 x^{2}-60 x+301$

Find the mistake, then find the correct answer. line $1 \quad x^{2}-6 x=-8$ line $2 \quad x^{2}-6 x+9=-8+9$ line $3 \quad(x-3)^{2}=1$ line $4 \quad x-3=\sqrt{1}$ line $5 \quad x-3=1$ line $6 \quad x-3+3=1+3$ line $7 \quad x=4$ line $8 \quad$ The solution set is $\{4\}$ .

Find the mistake, then find the correct answer. Solve for $\mathrm{x}: \mathrm{x}^{2}=50$ line $1 \quad \sqrt{x^{2}}=\sqrt{50}$ line $2 \quad x=2 \sqrt{5}$ or $x=-2 \sqrt{5}$ line 3 The solution set is $\{2 \sqrt{5},-2 \sqrt{5}\}$ .

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

Solve the equation by completing the square. - 0.7 m2+0.8 m+0.2=00.7 \mathrm{~m}^{2}+0.8 \mathrm{~m}+0.2=00.7 m2+0.8 m+0.2=0

Solve the equation. - 4y=1−6y4 y=\sqrt{1-6 y}4y=1−6y​

Graph the parabola. - x=y2+3x=y^{2}+3x=y2+3

True or false? The equation −x2=−36-x^{2}=-36−x2=−36 has no real solutions. If false, give the solution or solutions.

Solve the inequality, and graph the solution set. - 3y+5y−4≤0\frac{3 y+5}{y-4} \leq 0y−43y+5​≤0

Solve the equation by completing the square. - 4m2+15m=04 m^{2}+15 m=04m2+15m=0

Describe how the graph of y=x2−4y=x^{2}-4y=x2−4 differs from the graph of y=x2y=x^{2}y=x2 .

x=y2−9y+3x=y^{2}-9 y+3x=y2−9y+3

Solve for xxx . Assume that aaa and bbb represent positive real numbers. - (3x−4b)2=7a(3 x-4 b)^{2}=7 a(3x−4b)2=7a

A projectile is thrown upward so that its distance above the ground after ttt sec is given by h(t)=−13t2+390th(t)=-13 t^{2}+390 th(t)=−13t2+390t . After how many seconds does it reach its maximum height?

Choose the equation that matches the graph. -

Sketch the graph of the parabola. -

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−x−6=0x^{2}-x-6=0x2−x−6=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. - x2+3x−18=0x^{2}+3 x-18=0x2+3x−18=0

Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not actually solve. - w2−10w−6=0w^{2}-10 w-6=0w2−10w−6=0

For the quadratic function, tell whether the graph opens up or down and whether the graph is wider, narrower, or the same shape as the graph of f(x)=x2f(x)=x^{2}f(x)=x2 . - f(x)=18x2−9f(x)=\frac{1}{8} x^{2}-9f(x)=81​x2−9

Find the vertex of the parabola - f(x)=3x2−60x+301f(x)=3 x^{2}-60 x+301f(x)=3x2−60x+301

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

Solve the equation by completing the square. - $0.7 \mathrm{~m}^{2}+0.8 \mathrm{~m}+0.2=0$

Solve the equation. - $4 y=\sqrt{1-6 y}$

Graph the parabola. - $x=y^{2}+3$ $Graph the parabola. - x=y^{2}+3$

True or false? The equation $-x^{2}=-36$ has no real solutions. If false, give the solution or solutions.

Solve the inequality, and graph the solution set. - $\frac{3 y+5}{y-4} \leq 0$ $Solve the inequality, and graph the solution set. - \frac{3 y+5}{y-4} \leq 0$

Solve the equation by completing the square. - $4 m^{2}+15 m=0$

Describe how the graph of $y=x^{2}-4$ differs from the graph of $y=x^{2}$ .

$x=y^{2}-9 y+3$

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers. - $(3 x-4 b)^{2}=7 a$

A projectile is thrown upward so that its distance above the ground after $t$ sec is given by $h(t)=-13 t^{2}+390 t$ . After how many seconds does it reach its maximum height?

Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not actually solve. - $w^{2}-10 w-6=0$

For the quadratic function, tell whether the graph opens up or down and whether the graph is wider, narrower, or the same shape as the graph of $f(x)=x^{2}$ . - $f(x)=\frac{1}{8} x^{2}-9$

Find the vertex of the parabola - $f(x)=3 x^{2}-60 x+301$