Question 1

Use the square root property to solve the equation.
-$x^{2}-25=0$

Accepted Answer

A)  $\{5,-5\}$ 
B)  $\{13.5\}$ 
C)  $\{5\}$ 
D)  $\{4,-4\}$ 
A)  $\{5,-5\}$ 
B)  $\{13.5\}$ 
C)  $\{5\}$ 
D)  $\{4,-4\}$

Question 2

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.)
-$x= \pm \sqrt{r^{2}-y^{2}}$ for $r$

Accepted Answer

A)  $r= \pm \sqrt{x+y}$ 
B)  $r= \pm \sqrt{x^{2}+y^{2}}$ 
C)  $r= \pm \sqrt{x^{2}-y^{2}}$ 
D)  $r=x+y$ 
A)  $r= \pm \sqrt{x+y}$ 
B)  $r= \pm \sqrt{x^{2}+y^{2}}$ 
C)  $r= \pm \sqrt{x^{2}-y^{2}}$ 
D)  $r=x+y$

Question 3

Solve, and graph the solution set.
-$\frac{8}{p-3}<1$

Accepted Answer

A)  $ (3,11) $
  
B)  $ (\infty, 3) \cup(11, \infty) $
  
C)  $ [3,11] $
  
D)  $ (\infty, 3] \cup[11, \infty) $
  
A)  $ (3,11) $
  
B)  $ (\infty, 3) \cup(11, \infty) $
  
C)  $ [3,11] $
  
D)  $ (\infty, 3] \cup[11, \infty) $

Question 4

Mary lives on a corner lot. The neighborhood children have been cutting diagonally across her lawn instead of walking around the yard. If the diagonal distance across the lawn is 30 feet and the longer part of the sidewalk is twice the shorter length, how many feet are the children saving by cutting across the lawn? Round to the nearest foot if necessary.

Accepted Answer

A)  $17 \mathrm{ft}$ 
B)  $13 \mathrm{ft}$ 
C)  $40 \mathrm{ft}$ 
D)  $10 \mathrm{ft}$
Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate. 
A)  $17 \mathrm{ft}$ 
B)  $13 \mathrm{ft}$ 
C)  $40 \mathrm{ft}$ 
D)  $10 \mathrm{ft}$
Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate.

Question 5

Graph the parabola. Identify the vertex, axis, domain and range.
-$x=(y+1)^{2}-6$

Accepted Answer

A)  Vertex: (1, -9); Axis: $\mathrm{x}=-1$;
Domain: $(\infty, \infty)$; Range: $(\infty,-6]$
  
B)  Vertex: $(-6,-1)$; Axis : $y=-1$;
Domain: $(\infty,-6]$; Range: $(\infty, \infty)$
  
C)  Vertex: $(-1,-7)$; Axis: $\mathrm{x}=-1$;
Domain: $(\infty, \infty)$; Range: $[-6, \infty)$
 232
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D)  Vertex: $(-6,-1)$; Axis : $y=-1$;
Domain: $[-6, \infty)$; Range: $(\infty, \infty)$
  
A)  Vertex: (1, -9); Axis: $\mathrm{x}=-1$;
Domain: $(\infty, \infty)$; Range: $(\infty,-6]$
  
B)  Vertex: $(-6,-1)$; Axis : $y=-1$;
Domain: $(\infty,-6]$; Range: $(\infty, \infty)$
  
C)  Vertex: $(-1,-7)$; Axis: $\mathrm{x}=-1$;
Domain: $(\infty, \infty)$; Range: $[-6, \infty)$
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D)  Vertex: $(-6,-1)$; Axis : $y=-1$;
Domain: $[-6, \infty)$; Range: $(\infty, \infty)$

Question 6

Solve the inequality, and graph the solution set.
-$(a+5)(a-3)(a-7)>0$

Accepted Answer

A)  $(7, \infty)$
  
B)  $(-5,3) \cup(7, \infty)$
  
C)  $(-\infty, 3)$
  
D)  $(-\infty,-5) \cup(3,7)$
  
A)  $(7, \infty)$
  
B)  $(-5,3) \cup(7, \infty)$
  
C)  $(-\infty, 3)$
  
D)  $(-\infty,-5) \cup(3,7)$

Question 7

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it.
-$d^{2}-7 d+2=0$

Accepted Answer

A)  $(d+2)(d-1)=0$ 
B)  $(\mathrm{d}-1.4)^{2}=0$ 
C)  $(d+1)(d-3)=0$ 
D)  Cannot be solved by factoring 
A)  $(d+2)(d-1)=0$ 
B)  $(\mathrm{d}-1.4)^{2}=0$ 
C)  $(d+1)(d-3)=0$ 
D)  Cannot be solved by factoring

Question 8

Decide whether the graph of the equation opens up, down, to the left, or to the right; and whether it is wider, narrower, or the same shape as the graph of $f(x)=x^{2}\left(\right.$ or $\left.x=y^{2}\right)$.
-$f(x)=-8 x^{2}-7 x$

Accepted Answer

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

Question 9

Solve the problem. Round your answer to the nearest tenth, if necessary.
-A man rode a bicycle for $12 \mathrm{mi}$ and then hiked an additional $8 \mathrm{mi}$. The total time for the trip was 5 $\mathrm{hr}$. If his rate when he was riding a bicycle was $10 \mathrm{mph}$ faster than his rate walking, what was each rate?

Accepted Answer

A)  Bike: $13 \mathrm{mph}$; hike: $3 \mathrm{mph}$ 
B)  Bike: $14.5 \mathrm{mph}$; hike: $4.5 \mathrm{mph}$ 
C)  Bike: $12 \mathrm{mph}$; hike: $2 \mathrm{mph}$ 
D)  Bike: $11.5 \mathrm{mph}$; hike: $1.5 \mathrm{mph}$ 
A)  Bike: $13 \mathrm{mph}$; hike: $3 \mathrm{mph}$ 
B)  Bike: $14.5 \mathrm{mph}$; hike: $4.5 \mathrm{mph}$ 
C)  Bike: $12 \mathrm{mph}$; hike: $2 \mathrm{mph}$ 
D)  Bike: $11.5 \mathrm{mph}$; hike: $1.5 \mathrm{mph}$

Question 10

Choose the one alternative that best completes the statement or answers the question.
Use the zero factor property to solve the equation
-$x^{2}+2 x-15=0$

Accepted Answer

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

Question 11

To complete the square of $2 x^{2}+4 x=8$, is it ever a good idea to divide by the coefficient of $x^{2}$ ?

Accepted Answer

The answer of To complete the square of \(2 x^{2}+4...

Question 12

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

Accepted Answer

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

Question 13

Solve the equation by completing the square.
-$\mathrm{p}^{2}+3 \mathrm{p}-9=0$

Accepted Answer

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

Question 14

Use the ordered pairs $(1,12.85),(4,18.4)$, and $(8,18.8)$ to find a quadratic function that models the data. Round the values of $a, b$, and $c$ to two decimal places.

Accepted Answer

A)  $y=3.10 x^{2}-0.25 x+10.00$ 
B)  $y=0.25 x^{2}+3.10 x+10.00$ 
C)  $y=-0.25 x^{2}+3.10 x+10.00$ 
D)  $y=-3.1 x^{2}-0.25 x+10.00$ 
A)  $y=3.10 x^{2}-0.25 x+10.00$ 
B)  $y=0.25 x^{2}+3.10 x+10.00$ 
C)  $y=-0.25 x^{2}+3.10 x+10.00$ 
D)  $y=-3.1 x^{2}-0.25 x+10.00$

Question 15

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it.
-$16 k^{2}+40 k+25=0$

Accepted Answer

A)  $(4 \mathrm{k}+5)^{2}=0$ 
B)  Cannot be solved by factoring 
C)  $(4 \mathrm{k}+5)(4 \mathrm{k}-5)=0$ 
D)  $(16 \mathrm{k}-5)=0$ 
A)  $(4 \mathrm{k}+5)^{2}=0$ 
B)  Cannot be solved by factoring 
C)  $(4 \mathrm{k}+5)(4 \mathrm{k}-5)=0$ 
D)  $(16 \mathrm{k}-5)=0$

Question 16

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it.
-$f^{2}+5 f+7=0$

Accepted Answer

A)  $(f+7)(f-1)=0$ 
B)  $(\mathrm{f}+6)(\mathrm{f}-8)=0$ 
C)  Cannot be solved by factoring 
D)  $(\mathrm{f}-2.6)^{2}=0$ 
A)  $(f+7)(f-1)=0$ 
B)  $(\mathrm{f}+6)(\mathrm{f}-8)=0$ 
C)  Cannot be solved by factoring 
D)  $(\mathrm{f}-2.6)^{2}=0$

Question 17

Solve the equation $y=10 x^{2}+b x-7$ for $x$. If $y$ is positive and $b$ is positive, 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 positive, the first term

Question 18

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.)
-$A=\frac{1}{3} \pi r^{2}$ for $r$

Accepted Answer

A)  $r=\frac{3 \pi}{A}$ 
B)  $r= \pm \frac{\sqrt{3 \mathrm{~A} \pi}}{\pi}$ 
C)  $\mathrm{r}=3 \sqrt{\mathrm{A} \pi}$ 
D)  $r= \pm \frac{\sqrt{3 \mathrm{~A} \pi}}{3 \pi}$ 
A)  $r=\frac{3 \pi}{A}$ 
B)  $r= \pm \frac{\sqrt{3 \mathrm{~A} \pi}}{\pi}$ 
C)  $\mathrm{r}=3 \sqrt{\mathrm{A} \pi}$ 
D)  $r= \pm \frac{\sqrt{3 \mathrm{~A} \pi}}{3 \pi}$

Question 19

Use the square root property to solve the equation.
-$(x+19)^{2}=36$

Accepted Answer

A)  $\{-25,-13\}$ 
B)  $\{25,13\}$ 
C)  $\{-13\}$ 
D)  $\{-55\}$ 
A)  $\{-25,-13\}$ 
B)  $\{25,13\}$ 
C)  $\{-13\}$ 
D)  $\{-55\}$

Question 20

Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate.
-A book has pages that are $16 \mathrm{~cm}$ by $20 \mathrm{~cm}$. The printed matter on a page of the book must cover $140 \mathrm{~cm}^{2}$. If all margins are to be the same width, how wide should the margins be?

Accepted Answer

A)  $9 \mathrm{~cm}$ 
B)  $12 \mathrm{~cm}$ 
C)  $3 \mathrm{~cm}$ 
D)  $2 \mathrm{~cm}$ 
A)  $9 \mathrm{~cm}$ 
B)  $12 \mathrm{~cm}$ 
C)  $3 \mathrm{~cm}$ 
D)  $2 \mathrm{~cm}$

Use the square root property to solve the equation. - $x^{2}-25=0$

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.) - $x= \pm \sqrt{r^{2}-y^{2}}$ for $r$

Solve, and graph the solution set. - $\frac{8}{p-3}<1$ $Solve, and graph the solution set. - \frac{8}{p-3}<1$

Graph the parabola. Identify the vertex, axis, domain and range. - $x=(y+1)^{2}-6$ $Graph the parabola. Identify the vertex, axis, domain and range. - x=(y+1)^{2}-6$

Solve the inequality, and graph the solution set. - $(a+5)(a-3)(a-7)>0$

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - $d^{2}-7 d+2=0$

Decide whether the graph of the equation opens up, down, to the left, or to the right; and whether it is wider, narrower, or the same shape as the graph of $f(x)=x^{2}\left(\right.$ or $\left.x=y^{2}\right)$ . - $f(x)=-8 x^{2}-7 x$

Choose the one alternative that best completes the statement or answers the question. Use the zero factor property to solve the equation - $x^{2}+2 x-15=0$

To complete the square of $2 x^{2}+4 x=8$ , is it ever a good idea to divide by the coefficient of $x^{2}$ ?

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

Solve the equation by completing the square. - $\mathrm{p}^{2}+3 \mathrm{p}-9=0$

Use the ordered pairs $(1,12.85),(4,18.4)$ , and $(8,18.8)$ to find a quadratic function that models the data. Round the values of $a, b$ , and $c$ to two decimal places.

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - $16 k^{2}+40 k+25=0$

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - $f^{2}+5 f+7=0$

Solve the equation $y=10 x^{2}+b x-7$ for $x$ . If $y$ is positive and $b$ is positive, what, if anything, can you determine about the signs of the solutions? Explain your reasoning.

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.) - $A=\frac{1}{3} \pi r^{2}$ for $r$

Use the square root property to solve the equation. - $(x+19)^{2}=36$

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

Use the square root property to solve the equation. - x2−25=0x^{2}-25=0x2−25=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.) - x=±r2−y2x= \pm \sqrt{r^{2}-y^{2}}x=±r2−y2​ for rrr

Solve, and graph the solution set. - 8p−3<1\frac{8}{p-3}<1p−38​<1

Graph the parabola. Identify the vertex, axis, domain and range. - x=(y+1)2−6x=(y+1)^{2}-6x=(y+1)2−6

Solve the inequality, and graph the solution set. - (a+5)(a−3)(a−7)>0(a+5)(a-3)(a-7)>0(a+5)(a−3)(a−7)>0

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - d2−7d+2=0d^{2}-7 d+2=0d2−7d+2=0

Decide whether the graph of the equation opens up, down, to the left, or to the right; and whether it is wider, narrower, or the same shape as the graph of f(x)=x2(f(x)=x^{2}\left(\right.f(x)=x2( or x=y2)\left.x=y^{2}\right)x=y2) . - f(x)=−8x2−7xf(x)=-8 x^{2}-7 xf(x)=−8x2−7x

Choose the one alternative that best completes the statement or answers the question. Use the zero factor property to solve the equation - x2+2x−15=0x^{2}+2 x-15=0x2+2x−15=0

To complete the square of 2x2+4x=82 x^{2}+4 x=82x2+4x=8 , is it ever a good idea to divide by the coefficient of x2x^{2}x2 ?

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)=−5x2f(x)=-5 x^{2}f(x)=−5x2

Solve the equation by completing the square. - p2+3p−9=0\mathrm{p}^{2}+3 \mathrm{p}-9=0p2+3p−9=0

Use the ordered pairs (1,12.85),(4,18.4)(1,12.85),(4,18.4)(1,12.85),(4,18.4) , and (8,18.8)(8,18.8)(8,18.8) to find a quadratic function that models the data. Round the values of a,ba, ba,b , and ccc to two decimal places.

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - 16k2+40k+25=016 k^{2}+40 k+25=016k2+40k+25=0

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - f2+5f+7=0f^{2}+5 f+7=0f2+5f+7=0

Solve the equation y=10x2+bx−7y=10 x^{2}+b x-7y=10x2+bx−7 for xxx . If yyy is positive and bbb is positive, what, if anything, can you determine about the signs of the solutions? Explain your reasoning.

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.) - A=13πr2A=\frac{1}{3} \pi r^{2}A=31​πr2 for rrr

Use the square root property to solve the equation. - (x+19)2=36(x+19)^{2}=36(x+19)2=36