Question 1

Use the quadratic formula to
-$$\mathrm { z } ^ { 2 } + 10 \mathrm { z } + 3 = 0$$

Accepted Answer

A)  $- 5 \pm \sqrt { 22 }$ 
B)  $5 \pm \sqrt { 3 }$ 
C)  $- 10 + \sqrt { 3 }$ 
D)  $5 + \sqrt { 22 }$ 
A)  $- 5 \pm \sqrt { 22 }$ 
B)  $5 \pm \sqrt { 3 }$ 
C)  $- 10 + \sqrt { 3 }$ 
D)  $5 + \sqrt { 22 }$

Question 2

Use factoring to solve the equation
-$$9 m ^ { 2 } - 8 m = 0$$

Accepted Answer

A)  0 
B)  $\frac { 8 } { 9 } , - \frac { 8 } { 9 }$ 
C)  $\frac { 8 } { 9 } , 0$ 
D)  $- \frac { 8 } { 9 } , 0$ 
A)  0 
B)  $\frac { 8 } { 9 } , - \frac { 8 } { 9 }$ 
C)  $\frac { 8 } { 9 } , 0$ 
D)  $- \frac { 8 } { 9 } , 0$

Question 3

Graph
-$y=\sqrt[3]{x}+3$

Accepted Answer

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

Question 4

Use the quadratic formula to
-$$\mathrm { p } ^ { 2 } + \mathrm { p } - 9 = 0$$

Accepted Answer

A)  $\frac { - 1 \pm \sqrt { 37 } } { 2 }$ 
B)  $- 1 \pm \sqrt { 37 }$ 
C)  $\frac { 1 \pm \sqrt { 37 } } { 2 }$ 
D)  $\frac { - 1 \pm i \sqrt { 35 } } { 2 }$ 
A)  $\frac { - 1 \pm \sqrt { 37 } } { 2 }$ 
B)  $- 1 \pm \sqrt { 37 }$ 
C)  $\frac { 1 \pm \sqrt { 37 } } { 2 }$ 
D)  $\frac { - 1 \pm i \sqrt { 35 } } { 2 }$

Question 5

Provide an appropriate response.
-Which of the four methods of solving quadratic equations work(s) for any quadratic equation?

Accepted Answer

A)  Finding square roots and the quadratic formula 
B)  Completing the square and the quadratic formula 
C)  The quadratic formula and factoring 
D)  Factoring 
A)  Finding square roots and the quadratic formula 
B)  Completing the square and the quadratic formula 
C)  The quadratic formula and factoring 
D)  Factoring

Question 6

Provide an appropriate response.
-The following table has the inputs, x, and the outputs for three functions, f, g, and h. Use second differences to
determine which function is exactly quadratic, which is approximately quadratic, and which is not quadratic. $$\begin{array} { c | c | c | c } 
\mathrm { x } & \mathrm { f } ( \mathrm { x } ) & \mathrm { g } ( \mathrm { x } ) & \mathrm { h } ( \mathrm { x } ) \
\hline 0 & 8 & 0 & 0 \
1 & 8.6 & 0.5 & 2.9 \
2 & 9.2 & 2 & 12.3 \
3 & 9.8 & 4.5 & 26.8 \
4 & 10.4 & 8 & 47.4 \
5 & 11 & 12.5 & 75.2
\end{array}$$

Accepted Answer

f(x) is not quadrati

Question 7

Find the requested value.
-$f ( 2 )$ for $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } - 5 x + 1 , & \text { if } x \leq 2 \ x , & \text { if } x > 2 \end{array} \right.$

Accepted Answer

A)  13 
B)  2 
C)  $- 5$ 
D)  $- 7$ 
A)  13 
B)  2 
C)  $- 5$ 
D)  $- 7$

Question 8

Graph
-$y=\sqrt{x}-2$

Accepted Answer

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

Question 9

Suppose a life insurance policy costs $28 for the first unit of coverage and then $7 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?

Accepted Answer

A)  $42 
B)  $70 
C)  $91 
D)  $98 
A)  $42 
B)  $70 
C)  $91 
D)  $98

Question 10

Suppose the supply and demand for a certain videotape are given by: $$\text { supply: } p = \frac { 1 } { 6 } q ^ { 2 } ; \text { demand: } p = - \frac { 1 } { 6 } q ^ { 2 } + 37$$ where p is price and q is quantity. How many videotapes are demanded at a price of $22?

Accepted Answer

A)  About 8 videotapes 
B)  About 9 videotapes 
C)  About 11 videotapes 
D)  About 10 videotapes 
A)  About 8 videotapes 
B)  About 9 videotapes 
C)  About 11 videotapes 
D)  About 10 videotapes

Question 11

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 4 x ^ { 2 } - 288 x + 50$ where x is the number of watches repaired. How many watches must he repair to have the lowest cost?

Accepted Answer

A)  50 watches 
B)  36 watches 
C)  25 watches 
D)  40 watches 
A)  50 watches 
B)  36 watches 
C)  25 watches 
D)  40 watches

Question 12

Use the square root method to
-$$- 4 k ^ { 2 } + 64 = 0$$

Accepted Answer

A)  $- 36$ 
B)  $\pm 8$ 
C)  4 
D)  $\pm 4$ 
A)  $- 36$ 
B)  $\pm 8$ 
C)  4 
D)  $\pm 4$

Question 13

Use factoring to solve the equation
-$$20 y ^ { 2 } + 41 y + 20 = 0$$

Accepted Answer

A)  $- \frac { 1 } { 5 } , - \frac { 1 } { 4 }$ 
B)  $- \frac { 4 } { 5 } , - \frac { 5 } { 4 }$ 
C)  $\frac { 4 } { 5 } , \frac { 5 } { 4 }$ 
D)  $\frac { 4 } { 5 } , - \frac { 5 } { 4 }$ 
A)  $- \frac { 1 } { 5 } , - \frac { 1 } { 4 }$ 
B)  $- \frac { 4 } { 5 } , - \frac { 5 } { 4 }$ 
C)  $\frac { 4 } { 5 } , \frac { 5 } { 4 }$ 
D)  $\frac { 4 } { 5 } , - \frac { 5 } { 4 }$

Question 14

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The table shows the population of a certain city in various years. The population of the city $\mathrm { f } ( \mathrm { x } )$, in hundreds of thousands, can be modeled by $\mathrm { f } ( \mathrm { x } ) = \mathrm { ax } \mathrm { b }$, where x represents the number of years since 1995 . Estimate the population of the city in the year 2021. (You will first need to use regression to estimate the values of a and b).
$\begin{array}{l|ccccc}
\text { Year } & 1996 & 2000 & 2004 & 2008 & 2012 \
\hline \text { Population (hundreds of thousands) } & 3.2 & 4.1 & 5.7 & 9.6 & 14.1
\end{array}$

Accepted Answer

A)  1,177,277 
B)  1,240,963 
C)  1,318,550 
D)  1,365,641 
A)  1,177,277 
B)  1,240,963 
C)  1,318,550 
D)  1,365,641

Question 15

Use the graph of the function to estimate the x-intercepts.
-At Allied Electronics, production has begun on the $X - 15$ Computer Chip. The total revenue function is given by $R ( x ) = 50 x - 0.3 x ^ { 2 }$ and the total cost function is given by $C ( x ) = 8 x + 10$, where $x$ represents the number of boxes of computer chips produced. The total profit function, $P ( x )$, is such that $P ( x ) = R ( x ) - C ( x )$. Find $P ( x )$.

Accepted Answer

A)  $P ( x ) = - 0.3 x ^ { 2 } + 42 x - 10$ 
B)  $\mathrm { P } ( \mathrm { x } ) = 0.3 \mathrm { x } ^ { 2 } + 42 \mathrm { x } - 20$ 
C)  $P ( x ) = - 0.3 x ^ { 2 } + 34 x + 10$ 
D)  $\mathrm { P } ( \mathrm { x } ) = 0.3 \mathrm { x } ^ { 2 } + 34 \mathrm { x } - 30$ 
A)  $P ( x ) = - 0.3 x ^ { 2 } + 42 x - 10$ 
B)  $\mathrm { P } ( \mathrm { x } ) = 0.3 \mathrm { x } ^ { 2 } + 42 \mathrm { x } - 20$ 
C)  $P ( x ) = - 0.3 x ^ { 2 } + 34 x + 10$ 
D)  $\mathrm { P } ( \mathrm { x } ) = 0.3 \mathrm { x } ^ { 2 } + 34 \mathrm { x } - 30$

Question 16

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The population of a small town is given by the table. $\begin{array}{r|rrrr}
\text { Year } & 1980 & 1990 & 2000 & 2010 \
\hline \mathrm{P} & 7500 & 7513 & 7552 & 7617
\end{array}$

If the population is modeled by $\mathrm { p } ( \mathrm { t } ) = \mathrm { at } ^ { 2 } + \mathrm { b }$ where $\mathrm { t }$ is in years and $\mathrm { t } = 0$ corresponds to the year 1980 and $t = 1$ corresponds the year 1990 , find $a$.

Accepted Answer

A)  26 
B)  30 
C)  15 
D)  13 
A)  26 
B)  30 
C)  15 
D)  13

Question 17

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function.
-$$y = 3 x ^ { 2 } + 8 x - 16$$

Accepted Answer

A)  $( - 4,0 )$ 
B)  $( - 4,0 )$ and $\left( \frac { 4 } { 3 } , 0 \right)$ 
C)  No x-intercepts 
D)  $( 4,0 )$ and $\left( - \frac { 4 } { 3 } , 0 \right)$ 
A)  $( - 4,0 )$ 
B)  $( - 4,0 )$ and $\left( \frac { 4 } { 3 } , 0 \right)$ 
C)  No x-intercepts 
D)  $( 4,0 )$ and $\left( - \frac { 4 } { 3 } , 0 \right)$

Question 18

John owns a hot dog stand. He has found that his profit is given by the equation $P = - x ^ { 2 } + 80 x + 87$ , where x is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Accepted Answer

A)  23 hot dogs 
B)  47 hot dogs 
C)  40 hot dogs 
D)  41 hot dogs 
A)  23 hot dogs 
B)  47 hot dogs 
C)  40 hot dogs 
D)  41 hot dogs

Question 19

Graph
-$y=|7-x|$

Accepted Answer

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

Question 20

Suppose S varies directly as the cubed root of T, and tha $$\mathrm { S } = 24 \text { when } \mathrm { T } = 1 . \text { Find } \mathrm { T } \text { when } \mathrm { S } = 96$$ .

Accepted Answer

A)  64 
B)  1 
C)  4 
D)  24 
A)  64 
B)  1 
C)  4 
D)  24

Use the quadratic formula to - $\mathrm { z } ^ { 2 } + 10 \mathrm { z } + 3 = 0$

Use factoring to solve the equation - $9 m ^ { 2 } - 8 m = 0$

Graph - $y=\sqrt[3]{x}+3$ $Graph - y=\sqrt[3]{x}+3$

Use the quadratic formula to - $\mathrm { p } ^ { 2 } + \mathrm { p } - 9 = 0$

Provide an appropriate response. -Which of the four methods of solving quadratic equations work(s) for any quadratic equation?

Find the requested value. - $f ( 2 )$ for $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } - 5 x + 1 , & \text { if } x \leq 2 \\ x , & \text { if } x > 2 \end{array} \right.$

Graph - $y=\sqrt{x}-2$ $Graph - y=\sqrt{x}-2$

Suppose a life insurance policy costs $28 for the first unit of coverage and then $7 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?

Suppose the supply and demand for a certain videotape are given by: $\text { supply: } p = \frac { 1 } { 6 } q ^ { 2 } ; \text { demand: } p = - \frac { 1 } { 6 } q ^ { 2 } + 37$ where p is price and q is quantity. How many videotapes are demanded at a price of $22?

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 4 x ^ { 2 } - 288 x + 50$ where x is the number of watches repaired. How many watches must he repair to have the lowest cost?

Use the square root method to - $- 4 k ^ { 2 } + 64 = 0$

Use factoring to solve the equation - $20 y ^ { 2 } + 41 y + 20 = 0$

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function. - $y = 3 x ^ { 2 } + 8 x - 16$

John owns a hot dog stand. He has found that his profit is given by the equation $P = - x ^ { 2 } + 80 x + 87$ , where x is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Graph - $y=|7-x|$

Suppose S varies directly as the cubed root of T, and tha $\mathrm { S } = 24 \text { when } \mathrm { T } = 1 . \text { Find } \mathrm { T } \text { when } \mathrm { S } = 96$ .

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

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

Use the quadratic formula to - z2+10z+3=0\mathrm { z } ^ { 2 } + 10 \mathrm { z } + 3 = 0z2+10z+3=0

Use factoring to solve the equation - 9m2−8m=09 m ^ { 2 } - 8 m = 09m2−8m=0

Graph - y=x3+3y=\sqrt[3]{x}+3y=3x​+3

Use the quadratic formula to - p2+p−9=0\mathrm { p } ^ { 2 } + \mathrm { p } - 9 = 0p2+p−9=0

Provide an appropriate response. -Which of the four methods of solving quadratic equations work(s) for any quadratic equation?

Find the requested value. - f(2)f ( 2 )f(2) for f(x)={x2−5x+1, if x≤2x, if x>2f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } - 5 x + 1 , & \text { if } x \leq 2 \\ x , & \text { if } x > 2 \end{array} \right.f(x)={x2−5x+1,x,​ if x≤2 if x>2​

Graph - y=x−2y=\sqrt{x}-2y=x​−2

Suppose a life insurance policy costs $28 for the first unit of coverage and then $7 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c(x)=4x2−288x+50c ( x ) = 4 x ^ { 2 } - 288 x + 50c(x)=4x2−288x+50 where x is the number of watches repaired. How many watches must he repair to have the lowest cost?

Use the square root method to - −4k2+64=0- 4 k ^ { 2 } + 64 = 0−4k2+64=0

Use factoring to solve the equation - 20y2+41y+20=020 y ^ { 2 } + 41 y + 20 = 020y2+41y+20=0

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function. - y=3x2+8x−16y = 3 x ^ { 2 } + 8 x - 16y=3x2+8x−16

John owns a hot dog stand. He has found that his profit is given by the equation P=−x2+80x+87P = - x ^ { 2 } + 80 x + 87P=−x2+80x+87 , where x is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Graph - y=∣7−x∣y=|7-x|y=∣7−x∣

Suppose S varies directly as the cubed root of T, and tha S=24 when T=1. Find T when S=96\mathrm { S } = 24 \text { when } \mathrm { T } = 1 . \text { Find } \mathrm { T } \text { when } \mathrm { S } = 96S=24 when T=1. Find T when S=96 .

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

Use the quadratic formula to - $\mathrm { z } ^ { 2 } + 10 \mathrm { z } + 3 = 0$

Use factoring to solve the equation - $9 m ^ { 2 } - 8 m = 0$

Graph - $y=\sqrt[3]{x}+3$ $Graph - y=\sqrt[3]{x}+3$

Use the quadratic formula to - $\mathrm { p } ^ { 2 } + \mathrm { p } - 9 = 0$

Find the requested value. - $f ( 2 )$ for $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } - 5 x + 1 , & \text { if } x \leq 2 \\ x , & \text { if } x > 2 \end{array} \right.$

Graph - $y=\sqrt{x}-2$ $Graph - y=\sqrt{x}-2$

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 4 x ^ { 2 } - 288 x + 50$ where x is the number of watches repaired. How many watches must he repair to have the lowest cost?

Use the square root method to - $- 4 k ^ { 2 } + 64 = 0$

Use factoring to solve the equation - $20 y ^ { 2 } + 41 y + 20 = 0$

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function. - $y = 3 x ^ { 2 } + 8 x - 16$

John owns a hot dog stand. He has found that his profit is given by the equation $P = - x ^ { 2 } + 80 x + 87$ , where x is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Graph - $y=|7-x|$

Suppose S varies directly as the cubed root of T, and tha $\mathrm { S } = 24 \text { when } \mathrm { T } = 1 . \text { Find } \mathrm { T } \text { when } \mathrm { S } = 96$ .