Question 1

Find the vertex of the parabola
-$f(x)=4 x^{2}+16 x+12$

Accepted Answer

A)  $(-2,-4)$ 
B)  $(4,2)$ 
C)  $(2,4)$ 
D)  $(-4,-2)$ 
A)  $(-2,-4)$ 
B)  $(4,2)$ 
C)  $(2,4)$ 
D)  $(-4,-2)$

Question 2

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

Accepted Answer

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

Question 3

Solve the problem. Round your answer to the nearest tenth, if necessary.
-A jet plane traveling at a constant speed goes $1200 \mathrm{mi}$ with the wind, then turns around and travels for $1000 \mathrm{mi}$ against the wind. If the speed of the wind is a constant $50 \mathrm{mph}$, and the total flight took 4 hours, find the speed of the plane.

Accepted Answer

A)  $435 \mathrm{mph}$ 
B)  $605 \mathrm{mph}$ 
C)  $525 \mathrm{mph}$ 
D)  $550 \mathrm{mph}$ 
A)  $435 \mathrm{mph}$ 
B)  $605 \mathrm{mph}$ 
C)  $525 \mathrm{mph}$ 
D)  $550 \mathrm{mph}$

Question 4

Solve the inequality, and graph the solution set.
-$\frac{-4}{-5 x-2}>0$

Accepted Answer

A)  $ \left(-\frac{2}{5}, \infty\right) $
  
B)  $ (0, x) $
  
C)  $ \left(-\infty,-\frac{5}{2}\right) $
  
D)  $ \left(-\infty, \frac{2}{5}\right) $
  
A)  $ \left(-\frac{2}{5}, \infty\right) $
  
B)  $ (0, x) $
  
C)  $ \left(-\infty,-\frac{5}{2}\right) $
  
D)  $ \left(-\infty, \frac{2}{5}\right) $

Question 5

Solve the problem. Round your answer to the nearest tenth, when appropriate.
-A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in $t$ seconds is given by $s(t)=-16 t^{2}+177 t$. At what time or times will the ball be $221 \mathrm{ft}$ from the ground?

Accepted Answer

A)  171.8 and $182.2 \mathrm{sec}$ 
B)  $5.5 \mathrm{sec}$ 
C)  $11.1 \mathrm{sec}$ 
D)  1.4 and $9.6 \mathrm{sec}$ 
A)  171.8 and $182.2 \mathrm{sec}$ 
B)  $5.5 \mathrm{sec}$ 
C)  $11.1 \mathrm{sec}$ 
D)  1.4 and $9.6 \mathrm{sec}$

Question 6

To complete the square for an equation in the form $x^{2}-a x=b$, is it ever appropriate to subtract a positive number from each side?

Accepted Answer

The answer of To complete the square for an equation...

Question 7

$x-9=\frac{10}{x}$

Accepted Answer

A)  $\{-10,1\}$ 
B)  $\left\{1, \frac{1}{10}\right\}$ 
C)  $\{-1,10\}$ 
D)  $\left\{-\frac{1}{10}, 1\right\}$ 
A)  $\{-10,1\}$ 
B)  $\left\{1, \frac{1}{10}\right\}$ 
C)  $\{-1,10\}$ 
D)  $\left\{-\frac{1}{10}, 1\right\}$

Question 8

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

Accepted Answer

A)  $\left\{\frac{5+\sqrt{115}}{10}, \frac{5-\sqrt{115}}{10}\right\}$ 
B)  $\left\{\frac{-5+\sqrt{115}}{10}, \frac{-5-\sqrt{115}}{10}\right\}$ 
C)  $\left\{\frac{-5+\mathrm{i} \sqrt{115}}{10}, \frac{-5-\mathrm{i} \sqrt{115}}{10}\right\}$ 
D)  $\left\{\frac{5+\mathrm{i} \sqrt{115}}{10}, \frac{5-\mathrm{i} \sqrt{115}}{10}\right\}$ 
A)  $\left\{\frac{5+\sqrt{115}}{10}, \frac{5-\sqrt{115}}{10}\right\}$ 
B)  $\left\{\frac{-5+\sqrt{115}}{10}, \frac{-5-\sqrt{115}}{10}\right\}$ 
C)  $\left\{\frac{-5+\mathrm{i} \sqrt{115}}{10}, \frac{-5-\mathrm{i} \sqrt{115}}{10}\right\}$ 
D)  $\left\{\frac{5+\mathrm{i} \sqrt{115}}{10}, \frac{5-\mathrm{i} \sqrt{115}}{10}\right\}$

Question 9

Find the vertex of the parabola
-$f(x)=x^{2}-16 x+68$

Accepted Answer

A)  $(4,8)$ 
B)  $(8,4)$ 
C)  $(4,0)$ 
D)  $(0,8)$ 
A)  $(4,8)$ 
B)  $(8,4)$ 
C)  $(4,0)$ 
D)  $(0,8)$

Question 10

Tell what restrictions, if any, must be made on $\mathrm{d}$ and $\mathrm{k}$ (both real numbers) to guarantee that $\mathrm{t}$ is a real number. Assume that the denominator is not zero.
$t=\frac{\sqrt{d k}}{k}$

Accepted Answer

Either both must be

Question 11

Use the quadratic formula to solve the equation.
-$2 x^{2}=-5 x-7$

Accepted Answer

A)  $\left\{\frac{-5+\sqrt{31}}{4}, \frac{-5-\sqrt{31}}{4}\right\}$ 
B)  $\left\{\frac{-5+\mathrm{i} \sqrt{31}}{4}, \frac{-5-\mathrm{i} \sqrt{31}}{4}\right\}$ 
C)  $\left\{\frac{5+\mathrm{i} \sqrt{31}}{4}, \frac{5-\mathrm{i} \sqrt{31}}{4}\right\}$ 
D)  $\left\{\frac{5+\sqrt{31}}{4}, \frac{5-\sqrt{31}}{4}\right\}$ 
A)  $\left\{\frac{-5+\sqrt{31}}{4}, \frac{-5-\sqrt{31}}{4}\right\}$ 
B)  $\left\{\frac{-5+\mathrm{i} \sqrt{31}}{4}, \frac{-5-\mathrm{i} \sqrt{31}}{4}\right\}$ 
C)  $\left\{\frac{5+\mathrm{i} \sqrt{31}}{4}, \frac{5-\mathrm{i} \sqrt{31}}{4}\right\}$ 
D)  $\left\{\frac{5+\sqrt{31}}{4}, \frac{5-\sqrt{31}}{4}\right\}$

Question 12

Use the square root property to solve the equation.
-$(3 s+9)^{2}=25$

Accepted Answer

A)  $\left\{\frac{4}{3}, \frac{14}{3}\right\}$ 
B)  $\left\{-\frac{4}{3}, 0\right\}$ 
C)  $\left\{\frac{16}{3}\right\}$ 
D)  $\left\{-\frac{4}{3},-\frac{14}{3}\right\}$ 
A)  $\left\{\frac{4}{3}, \frac{14}{3}\right\}$ 
B)  $\left\{-\frac{4}{3}, 0\right\}$ 
C)  $\left\{\frac{16}{3}\right\}$ 
D)  $\left\{-\frac{4}{3},-\frac{14}{3}\right\}$

Question 13

Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate.
-The area of a square is $81 \mathrm{~cm}^{2}$. If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area $9 \mathrm{~cm}^{2}$ less than the area of the square. How much is added and subtracted?

Accepted Answer

A)  $4 \mathrm{~cm}$ 
B)  $9 \mathrm{~cm}$ 
C)  $3 \mathrm{~cm}$ 
D)  Cannot be determined without additional information 
A)  $4 \mathrm{~cm}$ 
B)  $9 \mathrm{~cm}$ 
C)  $3 \mathrm{~cm}$ 
D)  Cannot be determined without additional information

Question 14

Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate.
-A picture 9 in. by 12 in. is to be mounted on a piece of matte board so that there is an even amount of matte all around the picture. How wide will the border be if the area of the mounted picture is 238 in. $^{2}$ ?

Accepted Answer

A)  2 in. 
B)  $2.5 \mathrm{in}$. 
C)  3 in. 
D)  3.5 in. 
A)  2 in. 
B)  $2.5 \mathrm{in}$. 
C)  3 in. 
D)  3.5 in.

Question 15

Solve for $z$ in terms of the other variables.

Accepted Answer

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

Question 16

Solve the equation.
-$\sqrt{14 \mathrm{y}-21}=\mathrm{y}+2$

Accepted Answer

A)  $\{-4\}$ 
B)  $\{3\}$ 
C)  $\{5\}$ 
D)  $\{-5\}$ 
A)  $\{-4\}$ 
B)  $\{3\}$ 
C)  $\{5\}$ 
D)  $\{-5\}$

Question 17

Find the value of $k$ so that the equation will have exactly one rational solution.
-$9 x^{2}+k x+16=0$

Accepted Answer

A)  None 
B)  12 or -12 
C)  24 or -24 
D)  $24 \mathrm{i}$ or $-24 \mathrm{i}$ 
A)  None 
B)  12 or -12 
C)  24 or -24 
D)  $24 \mathrm{i}$ or $-24 \mathrm{i}$

Question 18

Which of the other three methods for solving quadratic equations is used to derive the quadratic formula?

Accepted Answer

Completing the squar

Question 19

$1-\frac{7}{\mathrm{x}}-\frac{18}{\mathrm{x}^{2}}=0$

Accepted Answer

A)  $\{9,2\}$ 
B)  $\{-9,-2\}$ 
C)  $\{-9,2\}$ 
D)  $\{9,-2\}$ 
A)  $\{9,2\}$ 
B)  $\{-9,-2\}$ 
C)  $\{-9,2\}$ 
D)  $\{9,-2\}$

Question 20

Solve the equation by completing the square.
-$a^{2}+8 a-33=0$

Accepted Answer

A)  $\{-22,-11\}$ 
B)  $\{3,-11\}$ 
C)  $\{6,-6\}$ 
D)  $\{-3,11\}$ 
A)  $\{-22,-11\}$ 
B)  $\{3,-11\}$ 
C)  $\{6,-6\}$ 
D)  $\{-3,11\}$

Find the vertex of the parabola - $f(x)=4 x^{2}+16 x+12$

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

Solve the inequality, and graph the solution set. - $\frac{-4}{-5 x-2}>0$ $Solve the inequality, and graph the solution set. - \frac{-4}{-5 x-2}>0$

Solve the problem. Round your answer to the nearest tenth, when appropriate. -A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in $t$ seconds is given by $s(t)=-16 t^{2}+177 t$ . At what time or times will the ball be $221 \mathrm{ft}$ from the ground?

To complete the square for an equation in the form $x^{2}-a x=b$ , is it ever appropriate to subtract a positive number from each side?

$x-9=\frac{10}{x}$

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

Find the vertex of the parabola - $f(x)=x^{2}-16 x+68$

Tell what restrictions, if any, must be made on $\mathrm{d}$ and $\mathrm{k}$ (both real numbers) to guarantee that $\mathrm{t}$ is a real number. Assume that the denominator is not zero. $t=\frac{\sqrt{d k}}{k}$

Use the quadratic formula to solve the equation. - $2 x^{2}=-5 x-7$

Use the square root property to solve the equation. - $(3 s+9)^{2}=25$

Solve for $z$ in terms of the other variables.

Solve the equation. - $\sqrt{14 \mathrm{y}-21}=\mathrm{y}+2$

Find the value of $k$ so that the equation will have exactly one rational solution. - $9 x^{2}+k x+16=0$

Which of the other three methods for solving quadratic equations is used to derive the quadratic formula?

$1-\frac{7}{\mathrm{x}}-\frac{18}{\mathrm{x}^{2}}=0$

Solve the equation by completing the square. - $a^{2}+8 a-33=0$

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

Find the vertex of the parabola - f(x)=4x2+16x+12f(x)=4 x^{2}+16 x+12f(x)=4x2+16x+12

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

Solve the inequality, and graph the solution set. - −4−5x−2>0\frac{-4}{-5 x-2}>0−5x−2−4​>0

To complete the square for an equation in the form x2−ax=bx^{2}-a x=bx2−ax=b , is it ever appropriate to subtract a positive number from each side?

x−9=10xx-9=\frac{10}{x}x−9=x10​

Find the nonreal complex solutions of the equation. - 5x2−5x+7=05 x^{2}-5 x+7=05x2−5x+7=0

Find the vertex of the parabola - f(x)=x2−16x+68f(x)=x^{2}-16 x+68f(x)=x2−16x+68

Tell what restrictions, if any, must be made on d\mathrm{d}d and k\mathrm{k}k (both real numbers) to guarantee that t\mathrm{t}t is a real number. Assume that the denominator is not zero. t=dkkt=\frac{\sqrt{d k}}{k}t=kdk​​

Use the quadratic formula to solve the equation. - 2x2=−5x−72 x^{2}=-5 x-72x2=−5x−7

Use the square root property to solve the equation. - (3s+9)2=25(3 s+9)^{2}=25(3s+9)2=25

Solve for zzz in terms of the other variables.

Solve the equation. - 14y−21=y+2\sqrt{14 \mathrm{y}-21}=\mathrm{y}+214y−21​=y+2

Find the value of kkk so that the equation will have exactly one rational solution. - 9x2+kx+16=09 x^{2}+k x+16=09x2+kx+16=0

Which of the other three methods for solving quadratic equations is used to derive the quadratic formula?

1−7x−18x2=01-\frac{7}{\mathrm{x}}-\frac{18}{\mathrm{x}^{2}}=01−x7​−x218​=0

Solve the equation by completing the square. - a2+8a−33=0a^{2}+8 a-33=0a2+8a−33=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

Find the vertex of the parabola - $f(x)=4 x^{2}+16 x+12$

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

Solve the inequality, and graph the solution set. - $\frac{-4}{-5 x-2}>0$ $Solve the inequality, and graph the solution set. - \frac{-4}{-5 x-2}>0$

To complete the square for an equation in the form $x^{2}-a x=b$ , is it ever appropriate to subtract a positive number from each side?

$x-9=\frac{10}{x}$

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

Find the vertex of the parabola - $f(x)=x^{2}-16 x+68$

Tell what restrictions, if any, must be made on $\mathrm{d}$ and $\mathrm{k}$ (both real numbers) to guarantee that $\mathrm{t}$ is a real number. Assume that the denominator is not zero. $t=\frac{\sqrt{d k}}{k}$

Use the quadratic formula to solve the equation. - $2 x^{2}=-5 x-7$

Use the square root property to solve the equation. - $(3 s+9)^{2}=25$

Solve for $z$ in terms of the other variables.

Solve the equation. - $\sqrt{14 \mathrm{y}-21}=\mathrm{y}+2$

Find the value of $k$ so that the equation will have exactly one rational solution. - $9 x^{2}+k x+16=0$

$1-\frac{7}{\mathrm{x}}-\frac{18}{\mathrm{x}^{2}}=0$

Solve the equation by completing the square. - $a^{2}+8 a-33=0$