Question 1

What are the advantages and disadvantages of the quadratic formula as a method of solving quadratic equations?

Accepted Answer

Answers will vary. One possibi

Question 2

Consider the rational inequality $\frac{-8}{-x^{2}-3}>0$. Without doing any work, give the solution set. (Hint: determine the sign of the numerator and denominator.)

Accepted Answer

A)  $(-3, \infty)$ 
B)  $\varnothing$ 
C)  $(-\infty,-8)$ 
D)  $(-\infty, \infty)$ 
A)  $(-3, \infty)$ 
B)  $\varnothing$ 
C)  $(-\infty,-8)$ 
D)  $(-\infty, \infty)$

Question 3

A jet plane traveling at a constant speed goes 1300 miles with the wind, then turns around and travels for 1100 miles against the wind. If the speed of the wind is $50 \mathrm{mph}$ and the total flight took 4 hours, find the speed of the plane in still air.

Accepted Answer

A)  $575 \mathrm{mph}$ 
B)  $600 \mathrm{mph}$ 
C)  $485 \mathrm{mph}$ 
D)  $655 \mathrm{mph}$ 
A)  $575 \mathrm{mph}$ 
B)  $600 \mathrm{mph}$ 
C)  $485 \mathrm{mph}$ 
D)  $655 \mathrm{mph}$

Question 4

Solve the inequality, and graph the solution set.
-$4 x^{2}-28 x+44 \leq 0$

Accepted Answer

A)  $\left(-\infty, \frac{7-\sqrt{5}}{2}\right] \cup\left[\frac{7+\sqrt{5}}{2}, \infty\right)$
  
B)  $\left[\frac{-7-\sqrt{5}}{2}, \frac{7+\sqrt{5}}{2}\right]$
  
C)  $\left(-\infty, \frac{7-\sqrt{5}}{2}\right) \cup\left(\frac{7+\sqrt{5}}{2}, \infty\right)$
  
D)  $\left[\frac{7-\sqrt{5}}{2}, \frac{7+\sqrt{5}}{2}\right]$
  
A)  $\left(-\infty, \frac{7-\sqrt{5}}{2}\right] \cup\left[\frac{7+\sqrt{5}}{2}, \infty\right)$
  
B)  $\left[\frac{-7-\sqrt{5}}{2}, \frac{7+\sqrt{5}}{2}\right]$
  
C)  $\left(-\infty, \frac{7-\sqrt{5}}{2}\right) \cup\left(\frac{7+\sqrt{5}}{2}, \infty\right)$
  
D)  $\left[\frac{7-\sqrt{5}}{2}, \frac{7+\sqrt{5}}{2}\right]$

Question 5

Find the value of $k$ so that the equation will have exactly one rational solution.
-$4 x^{2}+8 x+k=0$

Accepted Answer

A)  -4 
B)  None 
C)  $\frac{1}{2}$ 
D)  4 
A)  -4 
B)  None 
C)  $\frac{1}{2}$ 
D)  4

Question 6

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.
-$x^{2}+8 x+$

Accepted Answer

A)  $16 ;(x-4)^{2}$ 
B)  $64 ;(x+8)^{2}$ 
C)  $0 ;(x+4)^{2}$ 
D)  $16 ;(x+4)^{2}$ 
A)  $16 ;(x-4)^{2}$ 
B)  $64 ;(x+8)^{2}$ 
C)  $0 ;(x+4)^{2}$ 
D)  $16 ;(x+4)^{2}$

Question 7

Solve the equation.
-$\sqrt{2 x+15}-x=6$

Accepted Answer

A)  $\{-3\}$ 
B)  $\{7,-3\}$ 
C)  $\{-7\}$ 
D)  $\{-7,-3\}$ 
A)  $\{-3\}$ 
B)  $\{7,-3\}$ 
C)  $\{-7\}$ 
D)  $\{-7,-3\}$

Question 8

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.
-$-8 x^{2}+18 x+5=0$

Accepted Answer

A)  $\{-2.5,0.25\}$ 
B)  $\{5,18\}$ 
C)  $\{0.25,2.5\}$ 
D)  $\{-0.25,2.5\}$ 
A)  $\{-2.5,0.25\}$ 
B)  $\{5,18\}$ 
C)  $\{0.25,2.5\}$ 
D)  $\{-0.25,2.5\}$

Question 9

To solve the rational inequality $\frac{-2}{x-2} \geq 2$, you can first write the inequality with 0 on one side and the other side expressed as a single fraction. What value or values of $x$ make the numerator of that fraction equal to 0 ?

Accepted Answer

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

Question 10

Find the nonreal complex solutions of the equation.
-$6 x^{2}-7 x+5=0$

Accepted Answer

A)  $\left\{\frac{7+\sqrt{71}}{12}, \frac{7-\sqrt{71}}{12}\right\}$ 
B)  $\left\{\frac{-7+\mathrm{i} \sqrt{71}}{12}, \frac{-7-\mathrm{i} \sqrt{71}}{12}\right\}$ 
C)  $\left\{\frac{7+i \sqrt{71}}{12}, \frac{7-i \sqrt{71}}{12}\right\}$ 
D)  $\left\{\frac{-7+\sqrt{71}}{12}, \frac{-7-\sqrt{71}}{12}\right\}$ 
A)  $\left\{\frac{7+\sqrt{71}}{12}, \frac{7-\sqrt{71}}{12}\right\}$ 
B)  $\left\{\frac{-7+\mathrm{i} \sqrt{71}}{12}, \frac{-7-\mathrm{i} \sqrt{71}}{12}\right\}$ 
C)  $\left\{\frac{7+i \sqrt{71}}{12}, \frac{7-i \sqrt{71}}{12}\right\}$ 
D)  $\left\{\frac{-7+\sqrt{71}}{12}, \frac{-7-\sqrt{71}}{12}\right\}$

Question 11

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.)
-$c^{2}+d^{2}+f^{2}=g^{2}$, for $c$

Accepted Answer

A)  $\mathrm{c}=\mathrm{g}^{2}-\mathrm{d}^{2}-\mathrm{f}^{2}$ 
B)  $\mathrm{c}=\mathrm{g}-\mathrm{d}-\mathrm{f}$ 
C)  $c= \pm \sqrt{\mathrm{g}^{2}-\mathrm{d}^{2}-\mathrm{f}^{2}}$ 
D)  $c=-g+d+f$ 
A)  $\mathrm{c}=\mathrm{g}^{2}-\mathrm{d}^{2}-\mathrm{f}^{2}$ 
B)  $\mathrm{c}=\mathrm{g}-\mathrm{d}-\mathrm{f}$ 
C)  $c= \pm \sqrt{\mathrm{g}^{2}-\mathrm{d}^{2}-\mathrm{f}^{2}}$ 
D)  $c=-g+d+f$

Question 12

Solve by any method.
-$(-8 \mathrm{p}-5)^{2}=4(-8 \mathrm{p}-5)+12$

Accepted Answer

A)  $\left\{\frac{3}{8}, \frac{11}{8}\right\}$ 
B)  $\left\{-\frac{3}{8},-\frac{11}{8}\right\}$ 
C)  $\{-2,6\}$ 
D)  $\left\{\frac{7}{8},-\frac{1}{8}\right\}$ 
A)  $\left\{\frac{3}{8}, \frac{11}{8}\right\}$ 
B)  $\left\{-\frac{3}{8},-\frac{11}{8}\right\}$ 
C)  $\{-2,6\}$ 
D)  $\left\{\frac{7}{8},-\frac{1}{8}\right\}$

Question 13

Solve the equation.
-$\mathrm{s}=128+8 \sqrt{\mathrm{s}}$

Accepted Answer

A)  $\{256\}$ 
B)  $\{128\}$ 
C)  $\{192\}$ 
D)  $\{512\}$ 
A)  $\{256\}$ 
B)  $\{128\}$ 
C)  $\{192\}$ 
D)  $\{512\}$

Question 14

True or false? If $k=0$, then $x^{2}=k$ will have exactly one real solution. If false, give the correct number of real solutions.

Accepted Answer

A)  True 
B)  False; two 
C)  False; zero 
D)  False; three 
A)  True 
B)  False; two 
C)  False; zero 
D)  False; three

Question 15

$\frac{3}{3 x}-\frac{1}{x+1}=1$

Accepted Answer

A)  $\left\{\frac{1+\sqrt{5}}{2}, \frac{1-\sqrt{5}}{2}\right\}$ 
B)  $\left\{\frac{-1+\sqrt{5}}{2}, \frac{-1-\sqrt{5}}{2}\right\}$ 
C)  $\left\{\frac{-3+\sqrt{5}}{2}, \frac{-3-\sqrt{5}}{2}\right\}$ 
D)  $\varnothing$ 
A)  $\left\{\frac{1+\sqrt{5}}{2}, \frac{1-\sqrt{5}}{2}\right\}$ 
B)  $\left\{\frac{-1+\sqrt{5}}{2}, \frac{-1-\sqrt{5}}{2}\right\}$ 
C)  $\left\{\frac{-3+\sqrt{5}}{2}, \frac{-3-\sqrt{5}}{2}\right\}$ 
D)  $\varnothing$

Question 16

Which one of the following most closely resembles the graph of $f(x)=a(x-h)^{2}+k$ if $a>0, h0$ ?

Accepted Answer

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

Question 17

Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate.
-A square has an area of $49 \mathrm{in.}^{2}$. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of $45 \mathrm{in.}^{2}$. Find the dimensions of the rectangle.

Accepted Answer

A)  4 in. by 9 in. 
B)  5 in. by $10 \mathrm{in}$. 
C)  5 in. by 9 in. 
D)  Cannot be determined without additional information 
A)  4 in. by 9 in. 
B)  5 in. by $10 \mathrm{in}$. 
C)  5 in. by 9 in. 
D)  Cannot be determined without additional information

Question 18

Solve the equation by completing the square.
-$0.1 \mathrm{x}^{2}-0.2 \mathrm{x}-0.1=0$

Accepted Answer

A)  $\{1+\sqrt{2}\}$ 
B)  $\{1+\sqrt{2}, 1-\sqrt{2}\}$ 
C)  $\{2-\sqrt{2}\}$ 
D)  $\{2+\sqrt{2}, 2-\sqrt{2}\}$ 
A)  $\{1+\sqrt{2}\}$ 
B)  $\{1+\sqrt{2}, 1-\sqrt{2}\}$ 
C)  $\{2-\sqrt{2}\}$ 
D)  $\{2+\sqrt{2}, 2-\sqrt{2}\}$

Question 19

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 $f(x)=x^{2}$.
-$f(x)=7 x^{2}-5$

Accepted Answer

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

Question 20

Use the quadratic formula to solve the equation.
-$x^{2}+x+6=0$

Accepted Answer

A)  $\left\{\frac{1+\sqrt{23}}{2}, \frac{1-\sqrt{23}}{2}\right\}$ 
B)  $\left\{\frac{-1+\sqrt{23}}{2}, \frac{-1-\sqrt{23}}{2}\right\}$ 
C)  $\left\{\frac{-1+\mathrm{i} \sqrt{23}}{2}, \frac{-1-\mathrm{i} \sqrt{23}}{2}\right\}$ 
D)  $\left\{\frac{1+\mathrm{i} \sqrt{23}}{2}, \frac{1-\mathrm{i} \sqrt{23}}{2}\right\}$ 
A)  $\left\{\frac{1+\sqrt{23}}{2}, \frac{1-\sqrt{23}}{2}\right\}$ 
B)  $\left\{\frac{-1+\sqrt{23}}{2}, \frac{-1-\sqrt{23}}{2}\right\}$ 
C)  $\left\{\frac{-1+\mathrm{i} \sqrt{23}}{2}, \frac{-1-\mathrm{i} \sqrt{23}}{2}\right\}$ 
D)  $\left\{\frac{1+\mathrm{i} \sqrt{23}}{2}, \frac{1-\mathrm{i} \sqrt{23}}{2}\right\}$

What are the advantages and disadvantages of the quadratic formula as a method of solving quadratic equations?

Consider the rational inequality $\frac{-8}{-x^{2}-3}>0$ . Without doing any work, give the solution set. (Hint: determine the sign of the numerator and denominator.)

A jet plane traveling at a constant speed goes 1300 miles with the wind, then turns around and travels for 1100 miles against the wind. If the speed of the wind is $50 \mathrm{mph}$ and the total flight took 4 hours, find the speed of the plane in still air.

Solve the inequality, and graph the solution set. - $4 x^{2}-28 x+44 \leq 0$ $Solve the inequality, and graph the solution set. - 4 x^{2}-28 x+44 \leq 0$

Find the value of $k$ so that the equation will have exactly one rational solution. - $4 x^{2}+8 x+k=0$

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. - $x^{2}+8 x+$

Solve the equation. - $\sqrt{2 x+15}-x=6$

To solve the rational inequality $\frac{-2}{x-2} \geq 2$ , you can first write the inequality with 0 on one side and the other side expressed as a single fraction. What value or values of $x$ make the numerator of that fraction equal to 0 ?

Find the nonreal complex solutions of the equation. - $6 x^{2}-7 x+5=0$

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.) - $c^{2}+d^{2}+f^{2}=g^{2}$ , for $c$

Solve by any method. - $(-8 \mathrm{p}-5)^{2}=4(-8 \mathrm{p}-5)+12$

Solve the equation. - $\mathrm{s}=128+8 \sqrt{\mathrm{s}}$

True or false? If $k=0$ , then $x^{2}=k$ will have exactly one real solution. If false, give the correct number of real solutions.

$\frac{3}{3 x}-\frac{1}{x+1}=1$

Which one of the following most closely resembles the graph of $f(x)=a(x-h)^{2}+k$ if $a>0, h<0$ , and $\mathrm{k}>0$ ?

Solve the equation by completing the square. - $0.1 \mathrm{x}^{2}-0.2 \mathrm{x}-0.1=0$

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 $f(x)=x^{2}$ . - $f(x)=7 x^{2}-5$

Use the quadratic formula to solve the equation. - $x^{2}+x+6=0$

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

What are the advantages and disadvantages of the quadratic formula as a method of solving quadratic equations?

Consider the rational inequality −8−x2−3>0\frac{-8}{-x^{2}-3}>0−x2−3−8​>0 . Without doing any work, give the solution set. (Hint: determine the sign of the numerator and denominator.)

A jet plane traveling at a constant speed goes 1300 miles with the wind, then turns around and travels for 1100 miles against the wind. If the speed of the wind is 50mph50 \mathrm{mph}50mph and the total flight took 4 hours, find the speed of the plane in still air.

Solve the inequality, and graph the solution set. - 4x2−28x+44≤04 x^{2}-28 x+44 \leq 04x2−28x+44≤0

Find the value of kkk so that the equation will have exactly one rational solution. - 4x2+8x+k=04 x^{2}+8 x+k=04x2+8x+k=0

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+8x+x^{2}+8 x+x2+8x+

Solve the equation. - 2x+15−x=6\sqrt{2 x+15}-x=62x+15​−x=6

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. - −8x2+18x+5=0-8 x^{2}+18 x+5=0−8x2+18x+5=0

To solve the rational inequality −2x−2≥2\frac{-2}{x-2} \geq 2x−2−2​≥2 , you can first write the inequality with 0 on one side and the other side expressed as a single fraction. What value or values of xxx make the numerator of that fraction equal to 0 ?

Find the nonreal complex solutions of the equation. - 6x2−7x+5=06 x^{2}-7 x+5=06x2−7x+5=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.) - c2+d2+f2=g2c^{2}+d^{2}+f^{2}=g^{2}c2+d2+f2=g2 , for ccc

Solve by any method. - (−8p−5)2=4(−8p−5)+12(-8 \mathrm{p}-5)^{2}=4(-8 \mathrm{p}-5)+12(−8p−5)2=4(−8p−5)+12

Solve the equation. - s=128+8s\mathrm{s}=128+8 \sqrt{\mathrm{s}}s=128+8s​

True or false? If k=0k=0k=0 , then x2=kx^{2}=kx2=k will have exactly one real solution. If false, give the correct number of real solutions.

33x−1x+1=1\frac{3}{3 x}-\frac{1}{x+1}=13x3​−x+11​=1

Which one of the following most closely resembles the graph of f(x)=a(x−h)2+kf(x)=a(x-h)^{2}+kf(x)=a(x−h)2+k if a>0,h<0a>0, h<0a>0,h<0 , and k>0\mathrm{k}>0k>0 ?

Solve the equation by completing the square. - 0.1x2−0.2x−0.1=00.1 \mathrm{x}^{2}-0.2 \mathrm{x}-0.1=00.1x2−0.2x−0.1=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)=7x2−5f(x)=7 x^{2}-5f(x)=7x2−5

Use the quadratic formula to solve the equation. - x2+x+6=0x^{2}+x+6=0x2+x+6=0

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

Consider the rational inequality $\frac{-8}{-x^{2}-3}>0$ . Without doing any work, give the solution set. (Hint: determine the sign of the numerator and denominator.)

A jet plane traveling at a constant speed goes 1300 miles with the wind, then turns around and travels for 1100 miles against the wind. If the speed of the wind is $50 \mathrm{mph}$ and the total flight took 4 hours, find the speed of the plane in still air.

Solve the inequality, and graph the solution set. - $4 x^{2}-28 x+44 \leq 0$ $Solve the inequality, and graph the solution set. - 4 x^{2}-28 x+44 \leq 0$

Find the value of $k$ so that the equation will have exactly one rational solution. - $4 x^{2}+8 x+k=0$

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. - $x^{2}+8 x+$

Solve the equation. - $\sqrt{2 x+15}-x=6$

To solve the rational inequality $\frac{-2}{x-2} \geq 2$ , you can first write the inequality with 0 on one side and the other side expressed as a single fraction. What value or values of $x$ make the numerator of that fraction equal to 0 ?

Find the nonreal complex solutions of the equation. - $6 x^{2}-7 x+5=0$

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.) - $c^{2}+d^{2}+f^{2}=g^{2}$ , for $c$

Solve by any method. - $(-8 \mathrm{p}-5)^{2}=4(-8 \mathrm{p}-5)+12$

Solve the equation. - $\mathrm{s}=128+8 \sqrt{\mathrm{s}}$

True or false? If $k=0$ , then $x^{2}=k$ will have exactly one real solution. If false, give the correct number of real solutions.

$\frac{3}{3 x}-\frac{1}{x+1}=1$

Which one of the following most closely resembles the graph of $f(x)=a(x-h)^{2}+k$ if $a>0, h<0$ , and $\mathrm{k}>0$ ?

Solve the equation by completing the square. - $0.1 \mathrm{x}^{2}-0.2 \mathrm{x}-0.1=0$

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 $f(x)=x^{2}$ . - $f(x)=7 x^{2}-5$

Use the quadratic formula to solve the equation. - $x^{2}+x+6=0$