Question 1

Sketch the complete graph of the function.
-$y=8 x^{2}-32 x+38$

Accepted Answer

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

Question 2

Use the square root method to
-$$y ^ { 2 } - 20 = 0$$

Accepted Answer

A)  $\pm 2 \sqrt { 5 }$ 
B)  10 
C)  $\sqrt { 20 }$ 
D)  400 
A)  $\pm 2 \sqrt { 5 }$ 
B)  10 
C)  $\sqrt { 20 }$ 
D)  400

Question 3

In Country X, the average hourly wage in dollars from 1960 to 2010 can be modeled by $$f ( x ) = \left\{ \begin{array} { l l } 
0.075 ( x - 1960 ) + 0.39 & \text { if } 1960 \leq x < 1985 \
0.181 ( x - 1985 ) + 3.05 & \text { if } 1985 \leq x \leq 2010
\end{array} \right.$$ Use f to estimate the average hourly wages in 1965, 1985, and 2005.

Accepted Answer

A)  $0.77, $2.27, $6.67 
B)  $3.43, $0.39, $6.67 
C)  $0.77, $3.05, $6.67 
A)  $0.77, $2.27, $6.67 
B)  $3.43, $0.39, $6.67 
C)  $0.77, $3.05, $6.67

Question 4

Determine if the vertex of the graph is a maximum point or a minimum point.
-$y = - x ^ { 2 } + 4$

Accepted Answer

A)  Minimum 
B)  Maximum 
A)  Minimum 
B)  Maximum

Question 5

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 different years. Use regression to find values for a and b so that f(x) = axb models this data, where x represents the number of years since 1990 and f(x) is the
Population of the city in hundreds of thousands. Round your answers to 4 decimal places. $\begin{array}{l|ccccc}
\text { Year } & 1991 & 1995 & 1999 & 2003 & 2007 \
\hline \text { Population (hundreds of thousands) } & 3.2 & 4.1 & 5.7 & 9.6 & 14.1
\end{array}$

Accepted Answer

A)  $\mathrm { a } \approx 1.8506 , \mathrm {~b} \approx 0.5121$ 
B)  $a \approx 2.1375 , b \approx 0.4432$ 
C)  $\mathrm { a } \approx 1.7025 , \mathrm {~b} \approx 0.5375$ 
D)  $a \approx 2.6352 , b \approx 0.4756$ 
A)  $\mathrm { a } \approx 1.8506 , \mathrm {~b} \approx 0.5121$ 
B)  $a \approx 2.1375 , b \approx 0.4432$ 
C)  $\mathrm { a } \approx 1.7025 , \mathrm {~b} \approx 0.5375$ 
D)  $a \approx 2.6352 , b \approx 0.4756$

Question 6

Find a quadratic function that best fits the data. Give answers to the nearest hundredth.
-$\begin{array}{c|c|c|c|c|c}
\mathrm{x} & -2.4 & 34.8 & 65.6 & 102.3 & 253.6 \
\hline \mathrm{y} & 999.9 & 123.4 & 45.6 & 230.5 & 899.5
\end{array}$

Accepted Answer

A)  $y = 0.15 x ^ { 2 } - 38.67 x + 891.67$ 
B)  $y = 0.15 x ^ { 2 } + 38.67 x + 891.67$ 
C)  $y = 0.05 x ^ { 2 } - 13.25 x + 790.18$ 
D)  $y = 0.05 x ^ { 2 } + 13.25 x + 790.18$ 
A)  $y = 0.15 x ^ { 2 } - 38.67 x + 891.67$ 
B)  $y = 0.15 x ^ { 2 } + 38.67 x + 891.67$ 
C)  $y = 0.05 x ^ { 2 } - 13.25 x + 790.18$ 
D)  $y = 0.05 x ^ { 2 } + 13.25 x + 790.18$

Question 7

Solve the equation.
-$$| b + 5 | = 3$$

Accepted Answer

A)  $- 2$ 
B)  $- 8$ 
C)  $- 2 , - 8$ 
D)  2,8 
A)  $- 2$ 
B)  $- 8$ 
C)  $- 2 , - 8$ 
D)  2,8

Question 8

Use the quadratic formula to
-$$6 x ^ { 2 } + 12 x = - 3$$

Accepted Answer

A)  $\frac { - 12 \pm \sqrt { 2 } } { 2 }$ 
B)  $\frac { - 2 \pm \sqrt { 2 } } { 12 }$ 
C)  $\frac { - 2 \pm \sqrt { 2 } } { 2 }$ 
D)  $\frac { - 2 \pm \sqrt { 6 } } { 2 }$ 
A)  $\frac { - 12 \pm \sqrt { 2 } } { 2 }$ 
B)  $\frac { - 2 \pm \sqrt { 2 } } { 12 }$ 
C)  $\frac { - 2 \pm \sqrt { 2 } } { 2 }$ 
D)  $\frac { - 2 \pm \sqrt { 6 } } { 2 }$

Question 9

The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 15 ft from the light.

Accepted Answer

A)  $1 \frac { 2 } { 9 }$ foot-candles 
B)  $\frac { 2 } { 9 }$ foot-candle 
C)  $\frac { 1 } { 5 }$ foot-candle 
D)  2 foot-candles 
A)  $1 \frac { 2 } { 9 }$ foot-candles 
B)  $\frac { 2 } { 9 }$ foot-candle 
C)  $\frac { 1 } { 5 }$ foot-candle 
D)  2 foot-candles

Question 10

Determine if the vertex of the graph is a maximum point or a minimum point.
-$y = - ( x + 2 ) ^ { 2 } - 4$

Accepted Answer

A)  Maximum 
B)  Minimum 
A)  Maximum 
B)  Minimum

Question 11

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.
-$y=2 x^{2}-60 x+16$

Accepted Answer

A)  Vertex: $( 15 , - 434 )$
  
B)  Vertex: $( - 15 , - 434 )$
  
C)  Vertex: $( 30 , - 884 )$
  
D)  Vertex: $( 15 , - 390 )$
  
A)  Vertex: $( 15 , - 434 )$
  
B)  Vertex: $( - 15 , - 434 )$
  
C)  Vertex: $( 30 , - 884 )$
  
D)  Vertex: $( 15 , - 390 )$

Question 12

Assume that the elevation  E , in feet, of a sag in a proposed route is given by  E(x)=0.000036x2-0.29+1300 , where  x  represents the horizontal distance in feet along the proposed route and $0 \leq x \leq 5000$
For what  x -values is the elevation 1150 feet? Round your answer to the nearest foot.

Accepted Answer

A)   x=566 ft  or  x=7500 ft 
B)   x=556 ft  or  x=7510 ft 
C)   x=556 ft  or  x=7500 ft 
D)   x=566 ft or  x=7510 ft 
A)   x=566 ft  or  x=7500 ft 
B)   x=556 ft  or  x=7510 ft 
C)   x=556 ft  or  x=7500 ft 
D)   x=566 ft or  x=7510 ft

Question 13

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph?
-$f(x)=0.1 x^{2}-2 x-6$

Accepted Answer

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

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

No Yes

Question 14

You are given a graph of a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ for different values of $a , b$, and $c$. For this function,
a. Determine whether the discriminant is positive, negative, or zero.
b. Determine if there are 0,1 , or 2 real solutions to $f ( x ) = 0$.
c. Solve the equation $f ( x ) = 0$.
-

Accepted Answer

A)  a. positive
b. 2
C. $x = 1 , x = 2$ 
B)  a. zero
b. 2
c. $x = - 1 , x = 2$ 
C)  a. negative
b. 2
c. $x = - 1 , x = - 2$ 
D)  a. positive
b. 2
c. $x = - 1 , x = 2$ 
A)  a. positive
b. 2
C. $x = 1 , x = 2$ 
B)  a. zero
b. 2
c. $x = - 1 , x = 2$ 
C)  a. negative
b. 2
c. $x = - 1 , x = - 2$ 
D)  a. positive
b. 2
c. $x = - 1 , x = 2$

Question 15

Find a power function that models the data in the table. Round to three decimal places if necessary.
-$$\begin{array} { l | l l l l l } 
\mathrm { x } & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm { y } \mid & 9 & 14 & 18 & 19 & 23
\end{array}$$

Accepted Answer

A)  $y = 8.221 x ^ { 1.244 }$ 
B)  $y = 3.3 x + 6.7$ 
C)  $y = 0.565 x ^ { 9.208 }$ 
D)  $y = 9.208 x ^ { 0.565 }$ 
A)  $y = 8.221 x ^ { 1.244 }$ 
B)  $y = 3.3 x + 6.7$ 
C)  $y = 0.565 x ^ { 9.208 }$ 
D)  $y = 9.208 x ^ { 0.565 }$

Question 16

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal
places.
-$$x ^ { 2 } + 6 x - 72 = 0$$

Accepted Answer

A)  $- 12,6$ 
B)  $- 12,1$ 
C)  12,6 
D)  $12 , - 6$ 
A)  $- 12,6$ 
B)  $- 12,1$ 
C)  12,6 
D)  $12 , - 6$

Question 17

Suppose the price p of bolts is related to the quantity q that is demanded by: $p = 500 - 5 q ^ { 2 }$ where q is measured in hundreds of bolts. Suppose the supply function for bolts is given by $p = 5 q ^ { 2 }$ where q is the number of bolts (in hundreds) that are supplied at price p. Find the equilibrium supply.

Accepted Answer

A)  About 636 bolts 
B)  About 778 bolts 
C)  About 707 bolts 
D)  About 7 bolts 
A)  About 636 bolts 
B)  About 778 bolts 
C)  About 707 bolts 
D)  About 7 bolts

Question 18

Determine whether a linear or quadratic function would be a more appropriate model for the graphed data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the coefficient of $x ^ { 2 }$ should be positive or negative. $\text {DENTAL FLOSS USE}$
 
$\text {Years since 2000}$

Accepted Answer

A)  Linear; positive 
B)  Linear; negative 
C)  Quadratic; negative 
D)  Quadratic; positive 
A)  Linear; positive 
B)  Linear; negative 
C)  Quadratic; negative 
D)  Quadratic; positive

Question 19

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The table lists the distance traveled by a falling object, where t is the elapsed time in seconds and d is the distance in meters. $\begin{array}{r|rrrrrr}
\mathrm{t} & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{d} & 0 & 4.9 & 19.6 & 44.1 & 78.4 & 122.5
\end{array}$

\text { If the distance is modeled by } \mathrm { d } ( \mathrm { t } ) = \mathrm { at } ^ { 2 } \text {, find the distance traveled after } 13 \text { seconds. }
\end{array}\]

Accepted Answer

A)  828.1 meters 
B)  2704 meters 
C)  676 meters 
D)  4057.69 meters 
A)  828.1 meters 
B)  2704 meters 
C)  676 meters 
D)  4057.69 meters

Question 20

At Allied Electronics, production has begun on the  X-15  Computer Chip. The total cost function is given by  C(x)=2 x+13  and the total profit function is given by $P ( x ) = - 0.3 x ^ { 2 } + 50 x - 13$ where  x represents the number of boxes of computer chips produced. The total revenue function,  R(x) , is such that  R(x)=C(x)+P(x) . Find  R(x) .

Accepted Answer

A)  $R ( x ) = 54 x - 0.3 x ^ { 2 }$ 
B)  $R ( x ) = 51 x - 0.6 x ^ { 2 }$ 
C)  $R ( x ) = 52 x + 0.3 x ^ { 2 }$ 
D)  $R ( x ) = 52 x - 0.3 x ^ { 2 }$ 
A)  $R ( x ) = 54 x - 0.3 x ^ { 2 }$ 
B)  $R ( x ) = 51 x - 0.6 x ^ { 2 }$ 
C)  $R ( x ) = 52 x + 0.3 x ^ { 2 }$ 
D)  $R ( x ) = 52 x - 0.3 x ^ { 2 }$

Sketch the complete graph of the function. - $y=8 x^{2}-32 x+38$ $Sketch the complete graph of the function. - y=8 x^{2}-32 x+38$

Use the square root method to - $y ^ { 2 } - 20 = 0$

Determine if the vertex of the graph is a maximum point or a minimum point. - $y = - x ^ { 2 } + 4$

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - -2.4 34.8 65.6 102.3 253.6 999.9 123.4 45.6 230.5 899.5

Solve the equation. - $| b + 5 | = 3$

Use the quadratic formula to - $6 x ^ { 2 } + 12 x = - 3$

The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 15 ft from the light.

Determine if the vertex of the graph is a maximum point or a minimum point. - $y = - ( x + 2 ) ^ { 2 } - 4$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=2 x^{2}-60 x+16$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=2 x^{2}-60 x+16$

Assume that the elevation E , in feet, of a sag in a proposed route is given by E(x)=0.000036x²-0.29+1300 , where x represents the horizontal distance in feet along the proposed route and $0 \leq x \leq 5000$ For what x -values is the elevation 1150 feet? Round your answer to the nearest foot.

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph? - $f(x)=0.1 x^{2}-2 x-6$ $Graph the quadratic equation on [ [ - 10,10 ] \text { by } [ - 10,10 ] oes this window give a complete graph? - f(x)=0.1 x^{2}-2 x-6$

Find a power function that models the data in the table. Round to three decimal places if necessary. - 1 2 3 4 5 \mid 9 14 18 19 23

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $x ^ { 2 } + 6 x - 72 = 0$

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

Sketch the complete graph of the function. - y=8x2−32x+38y=8 x^{2}-32 x+38y=8x2−32x+38

Use the square root method to - y2−20=0y ^ { 2 } - 20 = 0y2−20=0

Determine if the vertex of the graph is a maximum point or a minimum point. - y=−x2+4y = - x ^ { 2 } + 4y=−x2+4

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - -2.4 34.8 65.6 102.3 253.6 999.9 123.4 45.6 230.5 899.5

Solve the equation. - ∣b+5∣=3| b + 5 | = 3∣b+5∣=3

Use the quadratic formula to - 6x2+12x=−36 x ^ { 2 } + 12 x = - 36x2+12x=−3

The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 15 ft from the light.

Determine if the vertex of the graph is a maximum point or a minimum point. - y=−(x+2)2−4y = - ( x + 2 ) ^ { 2 } - 4y=−(x+2)2−4

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=2x2−60x+16y=2 x^{2}-60 x+16y=2x2−60x+16

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)=0.1x2−2x−6f(x)=0.1 x^{2}-2 x-6f(x)=0.1x2−2x−6

Find a power function that models the data in the table. Round to three decimal places if necessary. - 1 2 3 4 5 \mid 9 14 18 19 23

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - x2+6x−72=0x ^ { 2 } + 6 x - 72 = 0x2+6x−72=0

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

Sketch the complete graph of the function. - $y=8 x^{2}-32 x+38$ $Sketch the complete graph of the function. - y=8 x^{2}-32 x+38$

Use the square root method to - $y ^ { 2 } - 20 = 0$

Determine if the vertex of the graph is a maximum point or a minimum point. - $y = - x ^ { 2 } + 4$

Solve the equation. - $| b + 5 | = 3$

Use the quadratic formula to - $6 x ^ { 2 } + 12 x = - 3$

Determine if the vertex of the graph is a maximum point or a minimum point. - $y = - ( x + 2 ) ^ { 2 } - 4$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=2 x^{2}-60 x+16$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=2 x^{2}-60 x+16$

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph? - $f(x)=0.1 x^{2}-2 x-6$ $Graph the quadratic equation on [ [ - 10,10 ] \text { by } [ - 10,10 ] oes this window give a complete graph? - f(x)=0.1 x^{2}-2 x-6$

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $x ^ { 2 } + 6 x - 72 = 0$