Question 1

Write the equation so that it is quadratic in form.
$6=-3 \sqrt{x}-2 x$

Accepted Answer

The answer of Write the equation so that it is...

Question 2

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.
-$x^{2}-\frac{2}{3} x+$

Accepted Answer

A)  $9 ;\left(x-\frac{1}{3}\right)^{2}$ 
B)  $\frac{1}{9} ;\left(x+\frac{1}{3}\right)^{2}$ 
C)  $-\frac{2}{3} x ;\left(x-\frac{1}{3}\right)^{2}$ 
D)  $\frac{1}{9} ;\left(x-\frac{1}{3}\right)^{2}$ 
A)  $9 ;\left(x-\frac{1}{3}\right)^{2}$ 
B)  $\frac{1}{9} ;\left(x+\frac{1}{3}\right)^{2}$ 
C)  $-\frac{2}{3} x ;\left(x-\frac{1}{3}\right)^{2}$ 
D)  $\frac{1}{9} ;\left(x-\frac{1}{3}\right)^{2}$

Question 3

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 $f(x)=x^{2}$.
-$f(x)=-x^{2}-18$

Accepted Answer

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

Question 4

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 5

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.
-$3 y^{2}=-2 y-5$

Accepted Answer

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

Question 6

Use the graph of a quadratic function to find the solution set of the equation or inequality.
-$x^{2}-13 x+40 \leq 0$

Accepted Answer

A)  $\{5,8\}$ 
B)  $(-\infty, 5) \cup(8, \infty)$ 
C)  $(5,8)$ 
D)  $[5,8]$ 
A)  $\{5,8\}$ 
B)  $(-\infty, 5) \cup(8, \infty)$ 
C)  $(5,8)$ 
D)  $[5,8]$

Question 7

Solve the problem. Round your answer to the nearest tenth, when appropriate.
-The position of an object moving in a straight line is given by $s(t)=2 t^{2}-3 t$, where $s$ is in meters and $t$ is the time in seconds the object has been in motion. How long will it take the object to move $13 \mathrm{~m}$ ?

Accepted Answer

A)  $3.4 \mathrm{sec}$ 
B)  $14.0 \mathrm{sec}$ 
C)  $29.9 \mathrm{sec}$ 
D)  $3.2 \mathrm{sec}$ 
A)  $3.4 \mathrm{sec}$ 
B)  $14.0 \mathrm{sec}$ 
C)  $29.9 \mathrm{sec}$ 
D)  $3.2 \mathrm{sec}$

Question 8

Solve the inequality, and graph the solution set.
-$2 x^{2}+3 x-20 \leq 0$

Accepted Answer

A)  $[-4, \infty)$
  
B)  $(-\infty,-4] \cup\left[\frac{5}{2}, \infty\right]$
  
C)  $\left[-\infty, \frac{5}{2}\right]$
  
D)  $\left[-4, \frac{5}{2}\right]$
  
A)  $[-4, \infty)$
  
B)  $(-\infty,-4] \cup\left[\frac{5}{2}, \infty\right]$
  
C)  $\left[-\infty, \frac{5}{2}\right]$
  
D)  $\left[-4, \frac{5}{2}\right]$

Question 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.)
-$2 n^{2}=-10 n-5$

Accepted Answer

A)  $\left\{\frac{-5+\sqrt{35}}{2}, \frac{-5-\sqrt{35}}{2}\right\}$ 
B)  $\left\{\frac{-5+\sqrt{15}}{2}, \frac{-5-\sqrt{15}}{2}\right\}$ 
C)  $\left\{\frac{-10+\sqrt{15}}{2}, \frac{-10-\sqrt{15}}{2}\right\}$ 
D)  $\left\{\frac{-5+\sqrt{15}}{4}, \frac{-5-\sqrt{15}}{4}\right\}$ 
A)  $\left\{\frac{-5+\sqrt{35}}{2}, \frac{-5-\sqrt{35}}{2}\right\}$ 
B)  $\left\{\frac{-5+\sqrt{15}}{2}, \frac{-5-\sqrt{15}}{2}\right\}$ 
C)  $\left\{\frac{-10+\sqrt{15}}{2}, \frac{-10-\sqrt{15}}{2}\right\}$ 
D)  $\left\{\frac{-5+\sqrt{15}}{4}, \frac{-5-\sqrt{15}}{4}\right\}$

Question 10

Ron can mow the lawn in two hours more time than Paul. Working together they can mow the lawn in 4 hours. How long does it take each of them working alone? Round your answers to the nearest tenth of an hour, if necessary.

Accepted Answer

A)  Paul: $6 \mathrm{hr}$
Ron: $10 \mathrm{hr}$ 
B)  Paul: $7.1 \mathrm{hr}$
Ron: $9.1 \mathrm{hr}$ 
C)  Paul: $9.1 \mathrm{hr}$
Ron: $7.1 \mathrm{hr}$ 
D)  Paul: $10 \mathrm{hr}$
Ron: $6 \mathrm{hr}$ 
A)  Paul: $6 \mathrm{hr}$
Ron: $10 \mathrm{hr}$ 
B)  Paul: $7.1 \mathrm{hr}$
Ron: $9.1 \mathrm{hr}$ 
C)  Paul: $9.1 \mathrm{hr}$
Ron: $7.1 \mathrm{hr}$ 
D)  Paul: $10 \mathrm{hr}$
Ron: $6 \mathrm{hr}$

Question 11

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

Accepted Answer

A)  $(-2,0)$ 
B)  $(2,-2)$ 
C)  $(2,2)$ 
D)  $(0,-2)$ 
A)  $(-2,0)$ 
B)  $(2,-2)$ 
C)  $(2,2)$ 
D)  $(0,-2)$

Question 12

If we apply the quadratic formula and find that the value of $b^{2}-4 a c$ is positive, what can we conclude?

Accepted Answer

A)  The equation has two real solutions. 
B)  The equation has two irrational solutions. 
C)  The equation has one rational solution. 
D)  The equation has no real solutions. 
A)  The equation has two real solutions. 
B)  The equation has two irrational solutions. 
C)  The equation has one rational solution. 
D)  The equation has no real solutions.

Question 13

Sketch the graph of the parabola.
-$y=x^{2}+4$

Accepted Answer

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

Question 14

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 $f(x)=x^{2}$.
-$f(x)=x^{2}+10$

Accepted Answer

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

Question 15

Use the graph of a quadratic function to find the solution set of the equation or inequality.
-

Accepted Answer

A)  $\{1,4\}$ 
B)  $(-\infty, 1) \cup(4, \infty)$ 
C)  $[1,4]$ 
D)  $(-\infty, 1] \cup[4, \infty)$ 
A)  $\{1,4\}$ 
B)  $(-\infty, 1) \cup(4, \infty)$ 
C)  $[1,4]$ 
D)  $(-\infty, 1] \cup[4, \infty)$

Question 16

Identify the vertex of the given parabola.
-$f(x)=-(x+4)^{2}-7$

Accepted Answer

A)  $(4,7)$ 
B)  $(-4,-7)$ 
C)  $(4,-7)$ 
D)  $(-4,7)$ 
A)  $(4,7)$ 
B)  $(-4,-7)$ 
C)  $(4,-7)$ 
D)  $(-4,7)$

Question 17

Graph the parabola.
-$f(x)=3 x^{2}+2 x+1$

Accepted Answer

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

Question 18

Use the square root property to solve the equation.
-$y^{2}=20$

Accepted Answer

A)  $\{2 \sqrt{5},-2 \sqrt{5}\}$ 
B)  $\{400\}$ 
C)  $\{10\}$ 
D)  $\{\sqrt{20}\}$ 
A)  $\{2 \sqrt{5},-2 \sqrt{5}\}$ 
B)  $\{400\}$ 
C)  $\{10\}$ 
D)  $\{\sqrt{20}\}$

Question 19

Define the term "quadratic equation".

Accepted Answer

An equation that can

Question 20

Solve by using the quadratic formula.
-$7 x=\sqrt{\frac{49 x-6}{2}}$

Accepted Answer

A)  $\left\{\frac{3}{14}\right\}$ 
B)  $\left\{\frac{2}{7}\right\}$ 
C)  $\left\{\frac{2}{7}, \frac{3}{14}\right\}$ 
D)  $\left\{-\frac{2}{7}, \frac{3}{14}\right\}$ 
A)  $\left\{\frac{3}{14}\right\}$ 
B)  $\left\{\frac{2}{7}\right\}$ 
C)  $\left\{\frac{2}{7}, \frac{3}{14}\right\}$ 
D)  $\left\{-\frac{2}{7}, \frac{3}{14}\right\}$

Write the equation so that it is quadratic in form. $6=-3 \sqrt{x}-2 x$

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form. - $x^{2}-\frac{2}{3} x+$

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 $f(x)=x^{2}$ . - $f(x)=-x^{2}-18$

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

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. - $3 y^{2}=-2 y-5$

Use the graph of a quadratic function to find the solution set of the equation or inequality. - $x^{2}-13 x+40 \leq 0$ $Use the graph of a quadratic function to find the solution set of the equation or inequality. - x^{2}-13 x+40 \leq 0$

Solve the inequality, and graph the solution set. - $2 x^{2}+3 x-20 \leq 0$ $Solve the inequality, and graph the solution set. - 2 x^{2}+3 x-20 \leq 0$

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.) - $2 n^{2}=-10 n-5$

Ron can mow the lawn in two hours more time than Paul. Working together they can mow the lawn in 4 hours. How long does it take each of them working alone? Round your answers to the nearest tenth of an hour, if necessary.

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

If we apply the quadratic formula and find that the value of $b^{2}-4 a c$ is positive, what can we conclude?

Sketch the graph of the parabola. - $y=x^{2}+4$ $Sketch the graph of the parabola. - y=x^{2}+4$

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 $f(x)=x^{2}$ . - $f(x)=x^{2}+10$

Use the graph of a quadratic function to find the solution set of the equation or inequality. -

Identify the vertex of the given parabola. - $f(x)=-(x+4)^{2}-7$

Graph the parabola. - $f(x)=3 x^{2}+2 x+1$ $Graph the parabola. - f(x)=3 x^{2}+2 x+1$

Use the square root property to solve the equation. - $y^{2}=20$

Define the term "quadratic equation".

Solve by using the quadratic formula. - $7 x=\sqrt{\frac{49 x-6}{2}}$

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

Write the equation so that it is quadratic in form. 6=−3x−2x6=-3 \sqrt{x}-2 x6=−3x​−2x

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form. - x2−23x+x^{2}-\frac{2}{3} x+x2−32​x+

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)=−x2−18f(x)=-x^{2}-18f(x)=−x2−18

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

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. - 3y2=−2y−53 y^{2}=-2 y-53y2=−2y−5

Use the graph of a quadratic function to find the solution set of the equation or inequality. - x2−13x+40≤0x^{2}-13 x+40 \leq 0x2−13x+40≤0

Solve the inequality, and graph the solution set. - 2x2+3x−20≤02 x^{2}+3 x-20 \leq 02x2+3x−20≤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.) - 2n2=−10n−52 n^{2}=-10 n-52n2=−10n−5

Ron can mow the lawn in two hours more time than Paul. Working together they can mow the lawn in 4 hours. How long does it take each of them working alone? Round your answers to the nearest tenth of an hour, if necessary.

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

If we apply the quadratic formula and find that the value of b2−4acb^{2}-4 a cb2−4ac is positive, what can we conclude?

Sketch the graph of the parabola. - y=x2+4y=x^{2}+4y=x2+4

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)=x2+10f(x)=x^{2}+10f(x)=x2+10

Use the graph of a quadratic function to find the solution set of the equation or inequality. -

Identify the vertex of the given parabola. - f(x)=−(x+4)2−7f(x)=-(x+4)^{2}-7f(x)=−(x+4)2−7

Graph the parabola. - f(x)=3x2+2x+1f(x)=3 x^{2}+2 x+1f(x)=3x2+2x+1

Use the square root property to solve the equation. - y2=20y^{2}=20y2=20

Define the term "quadratic equation".

Solve by using the quadratic formula. - 7x=49x−627 x=\sqrt{\frac{49 x-6}{2}}7x=249x−6​​

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

Write the equation so that it is quadratic in form. $6=-3 \sqrt{x}-2 x$

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form. - $x^{2}-\frac{2}{3} x+$

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 $f(x)=x^{2}$ . - $f(x)=-x^{2}-18$

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

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. - $3 y^{2}=-2 y-5$

Use the graph of a quadratic function to find the solution set of the equation or inequality. - $x^{2}-13 x+40 \leq 0$ $Use the graph of a quadratic function to find the solution set of the equation or inequality. - x^{2}-13 x+40 \leq 0$

Solve the inequality, and graph the solution set. - $2 x^{2}+3 x-20 \leq 0$ $Solve the inequality, and graph the solution set. - 2 x^{2}+3 x-20 \leq 0$

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.) - $2 n^{2}=-10 n-5$

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

If we apply the quadratic formula and find that the value of $b^{2}-4 a c$ is positive, what can we conclude?

Sketch the graph of the parabola. - $y=x^{2}+4$ $Sketch the graph of the parabola. - y=x^{2}+4$

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 $f(x)=x^{2}$ . - $f(x)=x^{2}+10$

Identify the vertex of the given parabola. - $f(x)=-(x+4)^{2}-7$

Graph the parabola. - $f(x)=3 x^{2}+2 x+1$ $Graph the parabola. - f(x)=3 x^{2}+2 x+1$

Use the square root property to solve the equation. - $y^{2}=20$

Solve by using the quadratic formula. - $7 x=\sqrt{\frac{49 x-6}{2}}$