Question 1

Find the exact solutions to the quadratic equation in the complex numbers.
-$$x ^ { 2 } - 4 x + 29 = 0$$

Accepted Answer

A)  $4 \pm 10 \mathrm { i }$ 
B)  $2 \pm 5 \mathrm { i }$ 
C)  $- 2 \pm 5 i$ 
D)  $7 , - 3$ 
A)  $4 \pm 10 \mathrm { i }$ 
B)  $2 \pm 5 \mathrm { i }$ 
C)  $- 2 \pm 5 i$ 
D)  $7 , - 3$

Question 2

Use the square root method to
-$$x ^ { 2 } + 2 = 171$$

Accepted Answer

A)  $85.5$ 
B)  $\pm 13$ 
C)  13 
D)  $\pm 12$ 
A)  $85.5$ 
B)  $\pm 13$ 
C)  13 
D)  $\pm 12$

Question 3

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

Accepted Answer

The disadvantage is that not all equatio

Question 4

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.
-$y=(x-4)^{2}+2$

Accepted Answer

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

Question 5

Suppose the price p of bolts is related to the quantity q that is demanded by: $$p = 550 - 4 q ^ { 2 }$$ where q is measured in hundreds of bolts. Find the price when the number of bolts demanded is 800.

Accepted Answer

A)  $309 
B)  $314 
C)  $294 
D)  $304 
A)  $309 
B)  $314 
C)  $294 
D)  $304

Question 6

Use factoring to solve the equation
-$$x ^ { 2 } + 2 x - 3 = 0$$

Accepted Answer

A)  $1 , - 3$ 
B)  $\sqrt { - 3 } , - \sqrt { - 3 }$ 
C)  $0 , - 3$ 
D)  $- 1,3$ 
A)  $1 , - 3$ 
B)  $\sqrt { - 3 } , - \sqrt { - 3 }$ 
C)  $0 , - 3$ 
D)  $- 1,3$

Question 7

Find the requested value.
-$f ( 0 )$ for $f ( x ) = \left\{ \begin{array} { l } x - 5 , \text { if } x < 6 \ 3 - x , \text { if } x \geq 6 \end{array} \right.$

Accepted Answer

A)  $- 5$ 
B)  1 
C)  $- 3$ 
D)  3 
A)  $- 5$ 
B)  1 
C)  $- 3$ 
D)  3

Question 8

Write the equation of the quadratic function whose graph is a parabola containing the given points.
-An egg is thrown upward from the top of a 128-foot-high building. The ball is 224 feet above ground level after 1 second, and it reaches ground level in 8 seconds. The height above the ground is a quadratic function of the
Time after the ball is thrown. Write the equation of this function.

Accepted Answer

A)  $y = - 16 x ^ { 2 } + 112 x + 128$ 
B)  $y = - 16 x ^ { 2 } + 144 x + 128$ 
C)  $y = - 16 x ^ { 2 } + 56 x + 128$ 
D)  $y = - 16 x ^ { 2 } + 16 x + 128$ 
A)  $y = - 16 x ^ { 2 } + 112 x + 128$ 
B)  $y = - 16 x ^ { 2 } + 144 x + 128$ 
C)  $y = - 16 x ^ { 2 } + 56 x + 128$ 
D)  $y = - 16 x ^ { 2 } + 16 x + 128$

Question 9

Given the solutions of a quadratic equation, is it possible to reconstruct the original equation? Why or why not?

Accepted Answer

No. Given the solutions of a quadratic e

Question 10

Use the square root method to
-$$25 x ^ { 2 } - 64 = 0$$

Accepted Answer

A)  $x = \pm \frac { 5 } { 8 }$ 
B)  $x = \frac { 8 } { 5 }$ 
C)  $x = \pm \frac { 8 } { 5 }$ 
D)  $x = \frac { \sqrt { 8 } } { 5 }$ 
A)  $x = \pm \frac { 5 } { 8 }$ 
B)  $x = \frac { 8 } { 5 }$ 
C)  $x = \pm \frac { 8 } { 5 }$ 
D)  $x = \frac { \sqrt { 8 } } { 5 }$

Question 11

Graph the function.
-$$\text { Graph } f ( x ) = \left\{ \begin{array} { l l } 
x - 1 , & \text { if } x \leq 1 \
1 - x , & \text { if } x > 1
\end{array} \right.$$

Accepted Answer

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

Question 12

Use the quadratic formula to
-$$p ^ { 2 } + 5 p - 5 = 0$$

Accepted Answer

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

Question 13

Solve the equation by completing the square.
-$$q ^ { 2 } + 8 q - 3 = 0$$

Accepted Answer

A)  $4 + \sqrt { 19 }$ 
B)  $- 4 \pm 2 \sqrt { 19 }$ 
C)  $- 1 \pm \sqrt { 19 }$ 
D)  $- 4 \pm \sqrt { 19 }$ 
A)  $4 + \sqrt { 19 }$ 
B)  $- 4 \pm 2 \sqrt { 19 }$ 
C)  $- 1 \pm \sqrt { 19 }$ 
D)  $- 4 \pm \sqrt { 19 }$

Question 14

The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft
Apart?

Accepted Answer

A)  2 lb 
B)  4 lb 
C)  1 lb 
D)  3 lb 
A)  2 lb 
B)  4 lb 
C)  1 lb 
D)  3 lb

Question 15

Graph
-$f(x)=|x+2|-1$

Accepted Answer

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

Question 16

Graph
-$y=x^{2 / 3}+4$

Accepted Answer

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

Question 17

A rule for estimating the number of board feet of lumber that can be cut from a log depends on the diameter of the log. To find the diameter,  \mathrm{d} , required to get 7 board feet of lumber, we use the equation $\left( \frac { d - 4 } { 4 } \right) ^ { 2 }$=49 .  Solve this equation for d. Are both answers reasonable?

Accepted Answer

A)   32,-24 ; No, only 32 feet is a reasonable answer. 
B)   11,-28 ; No, only 11 feet is a reasonable answer. 
C)   24,-32 ; No, only 24 feet is a reasonable answer. 
D)   28,-28 ; No, only 28 feet is a reasonable answer. 
A)   32,-24 ; No, only 32 feet is a reasonable answer. 
B)   11,-28 ; No, only 11 feet is a reasonable answer. 
C)   24,-32 ; No, only 24 feet is a reasonable answer. 
D)   28,-28 ; No, only 28 feet is a reasonable answer.

Question 18

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.
-$y=(x+4)^{2}$

Accepted Answer

A)  Vertex: $( 4,0 )$
  
B)  Vertex: $( 0,4 )$
  
C)  Vertex: $( - 4,0 )$
  
D)  Vertex: $( 0 , - 4 )$
  
A)  Vertex: $( 4,0 )$
  
B)  Vertex: $( 0,4 )$
  
C)  Vertex: $( - 4,0 )$
  
D)  Vertex: $( 0 , - 4 )$

Question 19

Find the requested value.
-$f ( 3 )$ for $f ( x ) = \left\{ \begin{array} { c l } 3 x + 1 & \text { if } x  5 \end{array} \right.$

Accepted Answer

A)  $- 9$ 
B)  21 
C)  9 
D)  4 
A)  $- 9$ 
B)  21 
C)  9 
D)  4

Question 20

Suppose a car rental company charges $94 for the first day and $44 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(3.5).

Accepted Answer

A)  $204 
B)  $226 
C)  $248 
D)  $154 
A)  $204 
B)  $226 
C)  $248 
D)  $154

Find the exact solutions to the quadratic equation in the complex numbers. - $x ^ { 2 } - 4 x + 29 = 0$

Use the square root method to - $x ^ { 2 } + 2 = 171$

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

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=(x-4)^{2}+2$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=(x-4)^{2}+2$

Suppose the price p of bolts is related to the quantity q that is demanded by: $p = 550 - 4 q ^ { 2 }$ where q is measured in hundreds of bolts. Find the price when the number of bolts demanded is 800.

Use factoring to solve the equation - $x ^ { 2 } + 2 x - 3 = 0$

Find the requested value. - $f ( 0 )$ for $f ( x ) = \left\{ \begin{array} { l } x - 5 , \text { if } x < 6 \\ 3 - x , \text { if } x \geq 6 \end{array} \right.$

Given the solutions of a quadratic equation, is it possible to reconstruct the original equation? Why or why not?

Use the square root method to - $25 x ^ { 2 } - 64 = 0$

Use the quadratic formula to - $p ^ { 2 } + 5 p - 5 = 0$

Solve the equation by completing the square. - $q ^ { 2 } + 8 q - 3 = 0$

The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft Apart?

Graph - $f(x)=|x+2|-1$

Graph - $y=x^{2 / 3}+4$ $Graph - y=x^{2 / 3}+4$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=(x+4)^{2}$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=(x+4)^{2}$

Find the requested value. - $f ( 3 )$ for $f ( x ) = \left\{ \begin{array} { c l } 3 x + 1 & \text { if } x < 1 \\ 3 x & \text { if } 3 \leq x \leq 5 \\ 3 - 4 x & \text { if } x > 5 \end{array} \right.$

Suppose a car rental company charges $94 for the first day and $44 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(3.5).

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 3: Quadratic, Piecewise-Defined, and Power Functions

Find the exact solutions to the quadratic equation in the complex numbers. - x2−4x+29=0x ^ { 2 } - 4 x + 29 = 0x2−4x+29=0

Use the square root method to - x2+2=171x ^ { 2 } + 2 = 171x2+2=171

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

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=(x−4)2+2y=(x-4)^{2}+2y=(x−4)2+2

Suppose the price p of bolts is related to the quantity q that is demanded by: p=550−4q2p = 550 - 4 q ^ { 2 }p=550−4q2 where q is measured in hundreds of bolts. Find the price when the number of bolts demanded is 800.

Use factoring to solve the equation - x2+2x−3=0x ^ { 2 } + 2 x - 3 = 0x2+2x−3=0

Find the requested value. - f(0)f ( 0 )f(0) for f(x)={x−5, if x<63−x, if x≥6f ( x ) = \left\{ \begin{array} { l } x - 5 , \text { if } x < 6 \\ 3 - x , \text { if } x \geq 6 \end{array} \right.f(x)={x−5, if x<63−x, if x≥6​

Given the solutions of a quadratic equation, is it possible to reconstruct the original equation? Why or why not?

Use the square root method to - 25x2−64=025 x ^ { 2 } - 64 = 025x2−64=0

Graph the function. - Graph f(x)={x−1, if x≤11−x, if x>1\text { Graph } f ( x ) = \left\{ \begin{array} { l l } x - 1 , & \text { if } x \leq 1 \\1 - x , & \text { if } x > 1\end{array} \right. Graph f(x)={x−1,1−x,​ if x≤1 if x>1​

Use the quadratic formula to - p2+5p−5=0p ^ { 2 } + 5 p - 5 = 0p2+5p−5=0

Solve the equation by completing the square. - q2+8q−3=0q ^ { 2 } + 8 q - 3 = 0q2+8q−3=0

The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft Apart?

Graph - f(x)=∣x+2∣−1f(x)=|x+2|-1f(x)=∣x+2∣−1

Graph - y=x2/3+4y=x^{2 / 3}+4y=x2/3+4

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=(x+4)2y=(x+4)^{2}y=(x+4)2

Suppose a car rental company charges $94 for the first day and $44 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(3.5).

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Find the exact solutions to the quadratic equation in the complex numbers. - $x ^ { 2 } - 4 x + 29 = 0$

Use the square root method to - $x ^ { 2 } + 2 = 171$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=(x-4)^{2}+2$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=(x-4)^{2}+2$

Suppose the price p of bolts is related to the quantity q that is demanded by: $p = 550 - 4 q ^ { 2 }$ where q is measured in hundreds of bolts. Find the price when the number of bolts demanded is 800.

Use factoring to solve the equation - $x ^ { 2 } + 2 x - 3 = 0$

Find the requested value. - $f ( 0 )$ for $f ( x ) = \left\{ \begin{array} { l } x - 5 , \text { if } x < 6 \\ 3 - x , \text { if } x \geq 6 \end{array} \right.$

Use the square root method to - $25 x ^ { 2 } - 64 = 0$

Use the quadratic formula to - $p ^ { 2 } + 5 p - 5 = 0$

Solve the equation by completing the square. - $q ^ { 2 } + 8 q - 3 = 0$

Graph - $f(x)=|x+2|-1$

Graph - $y=x^{2 / 3}+4$ $Graph - y=x^{2 / 3}+4$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=(x+4)^{2}$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=(x+4)^{2}$