Question 1

Solve the equation by completing the square.
-$$a ^ { 2 } + 14 a + 45 = 0$$

Accepted Answer

A)  $- 5 , - 9$ 
B)  $54 , - 9$ 
C)  5,9 
D)  $\sqrt { 45 } , - \sqrt { 45 }$ 
A)  $- 5 , - 9$ 
B)  $54 , - 9$ 
C)  5,9 
D)  $\sqrt { 45 } , - \sqrt { 45 }$ A

Question 2

If money is invested for 3 years , with interest compounded annually, the future value of the investment varies directly as the cube of ( $( 1 + r )$ r), where r is the annual interest rate. If the future value of the investment is $4499.46
When the interest rate is 4%, what rate gives a future value of $4244.83?

Accepted Answer

A)  4% 
B)  2% 
C)  0.02% 
D)  20% 
A)  4% 
B)  2% 
C)  0.02% 
D)  20% B

Question 3

Solve the equation by completing the square.
-$$z ^ { 2 } + 10 z + 4 = 0$$

Accepted Answer

A)  $5 \pm \sqrt { 4 }$ 
B)  $5 + \sqrt { 21 }$ 
C)  $- 5 \pm \sqrt { 21 }$ 
D)  $- 10 + \sqrt { 4 }$ 
A)  $5 \pm \sqrt { 4 }$ 
B)  $5 + \sqrt { 21 }$ 
C)  $- 5 \pm \sqrt { 21 }$ 
D)  $- 10 + \sqrt { 4 }$ C

Question 4

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph?
-$f(x)=-0.08 x^{2}+2 x-4$

Accepted Answer

A) 
  
B) 
  
C) 
$\text { No }$
  
D) 
$\text { Yes }$

Yes No 
A) 
  
B) 
  
C) 
$\text { No }$
  
D) 
$\text { Yes }$

Yes No

Question 5

The demand equation for a certain product is $\mathrm { P } = 75 - 0.001 \mathrm { x }$, where $\mathrm { x }$ is the number of units sold per week and $\mathrm { P }$ is the price in dollars at which one is sold. The weekly revenue $R$ is given by $R = x P$. What number of units sold produces a weekly revenue of $\$ 60,000$ ?

Accepted Answer

A)  74,191 units 
B)  59,925,000 units 
C)  792 units 
D)  809 units 
A)  74,191 units 
B)  59,925,000 units 
C)  792 units 
D)  809 units

Question 6

Find the exact solutions to the quadratic equation in the complex numbers.
-$$5 x ^ { 2 } + 55 = 0$$

Accepted Answer

A)  $\pm i \sqrt { 11 }$ 
B)  $\pm 11 \mathrm { i }$ 
C)  $27.5$ 
D)  $\pm \sqrt { 11 }$ 
A)  $\pm i \sqrt { 11 }$ 
B)  $\pm 11 \mathrm { i }$ 
C)  $27.5$ 
D)  $\pm \sqrt { 11 }$

Question 7

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The percent of people who say they plan to stay in the same job position until they retire has decreased over recent years, as shown in the table below. $$\begin{array} { c | c c c c c c } 
\text { Year } & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 \
\hline \text { Percent } & 42 & 38 & 35 & 34 & 30 & 26
\end{array}$$ Find a power function that models the data in the table using an input equal to the number of years from 2000.
According to the unrounded model, in what year will only 23% of people plan to stay in the same job position until
Retirement?

Accepted Answer

A)  2011 
B)  2015 
C)  2013 
D)  2016 
A)  2011 
B)  2015 
C)  2013 
D)  2016

Question 8

The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the intensity be at a distance of
3 miles? Round your answer to the nearest unit.

Accepted Answer

A)  3539 units 
B)  3520 units 
C)  3556 units 
D)  3582 units 
A)  3539 units 
B)  3520 units 
C)  3556 units 
D)  3582 units

Question 9

Find the exact solutions to the quadratic equation in the complex numbers.
-$$( 2 x - 1 ) ^ { 2 } + 3 = 0$$

Accepted Answer

A)  $\frac { 1 \pm \sqrt { 3 } } { 2 }$ 
B)  $2 \pm 2 \mathrm { i } \sqrt { 3 }$ 
C)  $\frac { 1 \pm 3 i } { 2 }$ 
D)  $\frac { 1 \pm i \sqrt { 3 } } { 2 }$ 
A)  $\frac { 1 \pm \sqrt { 3 } } { 2 }$ 
B)  $2 \pm 2 \mathrm { i } \sqrt { 3 }$ 
C)  $\frac { 1 \pm 3 i } { 2 }$ 
D)  $\frac { 1 \pm i \sqrt { 3 } } { 2 }$

Question 10

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The table shows the number of new cases of a certain disease among women in six consecutive years. Data are in thousands rounded to the nearest hundred. $\begin{array} { l c } \underline { \text { Year } } & \text { New Cases (thousands) } \ 2005 & 3.0 \ 2006 & 3.4 \ 2007 & 4.6 \ 2008 & 5.4 \ 2009 & 6.0 \ 2010 & 16.1 \end{array}$
Let $x = 1$ correspond to 2005 and let $y$ be the number of new cases (in thousands) among women in year x. Find a quadratic function to model the data. Round to three decimal places if necessary.

Accepted Answer

A)  $y = 6.69 x ^ { 2 } - 3.645 x + 0.823$ 
B)  $y = 0.823 x ^ { 2 } - 3.645 x + 6.69$ 
C)  $y = 0.945 x ^ { 2 } - 5.212 x + 8.921$ 
D)  $y = 0.623 x ^ { 2 } - 5.645 x + 8.69$ 
A)  $y = 6.69 x ^ { 2 } - 3.645 x + 0.823$ 
B)  $y = 0.823 x ^ { 2 } - 3.645 x + 6.69$ 
C)  $y = 0.945 x ^ { 2 } - 5.212 x + 8.921$ 
D)  $y = 0.623 x ^ { 2 } - 5.645 x + 8.69$

Question 11

The distance an object is from the ground after being tossed from a hot air balloon 830 feet in the air is a function of time: $y = - 16.1 t ^ { 2 } + 5.8 t + 830$ , where y is height and t is the amount of time the object has been in the
Air) Predict the height of the object after 5.5 seconds. Round to the nearest hundredth.

Accepted Answer

A)  311.08 ft 
B)  0.00 ft 
C)  773.35 ft 
D)  374.88 ft 
A)  311.08 ft 
B)  0.00 ft 
C)  773.35 ft 
D)  374.88 ft

Question 12

Graph the function.
-$$\text { Graph } f ( x ) = \left\{ \begin{aligned}
x , & \text { if } x \leq - 3 \
- x , & \text { if } x > - 3
\end{aligned} \right.$$

Accepted Answer

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

Question 13

Determine if the graph of the function is concave up or concave down
-$f ( x ) = - 3 x ^ { 2 } - 3 x - 9$

Accepted Answer

A)  Concave up 
B)  Concave down 
A)  Concave up 
B)  Concave down

Question 14

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The following points form a quadratic relationship: (1, 5.0), (2, 4.4), (3, 4.3), (4, 4.2), (5, 4.6), (6, 4.8), (7, 5.4), (8, 6.2) . The x-coordinates are the years a particular company has been in operation and the y-coordinates are the
Profit, in millions, for that year. Find the quadratic function that models the profit in millions as a function of x,
The number of years of operation. Round to three decimal places.

Accepted Answer

A)  $y = 0.099 x ^ { 2 } + 1.254 x - 3.512$ 
B)  $y = 0.101 x ^ { 2 } - 0.723 x + 5.552$ 
C)  $y = 0.203 x ^ { 2 } - 0.945 x + 7.098$ 
D)  $y = - 0.003 x ^ { 2 } + 0.145 x - 0.892$ 
A)  $y = 0.099 x ^ { 2 } + 1.254 x - 3.512$ 
B)  $y = 0.101 x ^ { 2 } - 0.723 x + 5.552$ 
C)  $y = 0.203 x ^ { 2 } - 0.945 x + 7.098$ 
D)  $y = - 0.003 x ^ { 2 } + 0.145 x - 0.892$

Question 15

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal
places.
-$$2 x ^ { 2 } + 6 x = - 1$$

Accepted Answer

A)  $0.158 , - 3.158$ 
B)  $- 0.089 , - 1.411$ 
C)  $- 0.177 , - 2.823$ 
D)  $- 1.677 , - 4.323$ 
A)  $0.158 , - 3.158$ 
B)  $- 0.089 , - 1.411$ 
C)  $- 0.177 , - 2.823$ 
D)  $- 1.677 , - 4.323$

Question 16

The table lists the amount of emissions of a certain pollutant in millions of tons. $\begin{array}{r|cccc}
\text { Year } & 1990 & 1995 & 2000 & 2005 \
\hline \mathrm{P} & 18.8 & 22.6 & 26.0 & 29.0
\end{array}$

If the amount of emissions is modeled by a function of the form $\mathrm { f } ( \mathrm { x } ) = \mathrm { ax } { } ^ { 2 } + \mathrm { bx } + \mathrm { c }$ where $\mathrm { x }$ is the year, estimate tl year in which the amount of emissions will be $10.0$ million tons.

Accepted Answer

A)  2060 
B)  2100 
C)  2085 
D)  2030 
A)  2060 
B)  2100 
C)  2085 
D)  2030

Question 17

Solve the equation.
-$$| x + 8 | = x ^ { 2 } + 8 x$$

Accepted Answer

A)  $- 8 , - 1$ 
B)  $- 8,1$ 
C)  $- 8 , - 1,1$ 
D)  $- 1,1$ 
A)  $- 8 , - 1$ 
B)  $- 8,1$ 
C)  $- 8 , - 1,1$ 
D)  $- 1,1$

Question 18

Use factoring to solve the equation
-$$4 x ^ { 2 } - 24 x + 32 = 0$$

Accepted Answer

A)  $4,2,4$ 
B)  2,4 
C)  $- 2 , - 4$ 
D)  $0,2,4$ 
A)  $4,2,4$ 
B)  2,4 
C)  $- 2 , - 4$ 
D)  $0,2,4$

Question 19

Graph the function.
-$$\mathrm { f } ( \mathrm { x } ) = \left\{ \begin{array} { l l } 
\mathrm { x } ^ { 2 } - 9 , & \text { if } \mathrm { x } < - 1 \
0 , & \text { if } - 1 \leq \mathrm { x } \leq 1 \
\mathrm { x } ^ { 2 } + 9 , & \text { if } 1 < \mathrm { x }
\end{array} \right.$$

Accepted Answer

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

Question 20

Write the equation of the quadratic function whose graph is a parabola containing the given points.
-$( 0,1 ) , ( 2,6 ) , ( - 3,8.5 )$

Accepted Answer

A)  $y = x ^ { 2 } + x + 1.5$ 
B)  $y = x ^ { 2 } + 5 x - 1$ 
C)  $y = x ^ { 2 } - 0.5 x + 1$ 
D)  $y = x ^ { 2 } + 0.5 x + 1$ 
A)  $y = x ^ { 2 } + x + 1.5$ 
B)  $y = x ^ { 2 } + 5 x - 1$ 
C)  $y = x ^ { 2 } - 0.5 x + 1$ 
D)  $y = x ^ { 2 } + 0.5 x + 1$

Solve the equation by completing the square. - $a ^ { 2 } + 14 a + 45 = 0$

Solve the equation by completing the square. - $z ^ { 2 } + 10 z + 4 = 0$

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph? - $f(x)=-0.08 x^{2}+2 x-4$ $Graph the quadratic equation on [ [ - 10,10 ] \text { by } [ - 10,10 ] oes this window give a complete graph? - f(x)=-0.08 x^{2}+2 x-4$

Find the exact solutions to the quadratic equation in the complex numbers. - $5 x ^ { 2 } + 55 = 0$

The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the intensity be at a distance of 3 miles? Round your answer to the nearest unit.

Find the exact solutions to the quadratic equation in the complex numbers. - $( 2 x - 1 ) ^ { 2 } + 3 = 0$

Determine if the graph of the function is concave up or concave down - $f ( x ) = - 3 x ^ { 2 } - 3 x - 9$

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $2 x ^ { 2 } + 6 x = - 1$

Solve the equation. - $| x + 8 | = x ^ { 2 } + 8 x$

Use factoring to solve the equation - $4 x ^ { 2 } - 24 x + 32 = 0$

Write the equation of the quadratic function whose graph is a parabola containing the given points. - $( 0,1 ) , ( 2,6 ) , ( - 3,8.5 )$

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

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

Solve the equation by completing the square. - a2+14a+45=0a ^ { 2 } + 14 a + 45 = 0a2+14a+45=0

Solve the equation by completing the square. - z2+10z+4=0z ^ { 2 } + 10 z + 4 = 0z2+10z+4=0

Graph the quadratic equation on [ [−10,10] by [−10,10][ - 10,10 ] \text { by } [ - 10,10 ][−10,10] by [−10,10] oes this window give a complete graph? - f(x)=−0.08x2+2x−4f(x)=-0.08 x^{2}+2 x-4f(x)=−0.08x2+2x−4

Find the exact solutions to the quadratic equation in the complex numbers. - 5x2+55=05 x ^ { 2 } + 55 = 05x2+55=0