Question 1

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

Accepted Answer

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

Question 2

If 5000 feet of fencing are used to enclose a rectangular field, the resulting area of the field is  A=x(2500-x) , where  x  is the width of the pen. What is the maximum possible area of the pen?

Accepted Answer

A)   62,500ft2 
B)   1,562,500ft2 
C)   1250ft2 
D)   31,250ft2 
A)   62,500ft2 
B)   1,562,500ft2 
C)   1250ft2 
D)   31,250ft2

Question 3

Graph
-$$f ( x ) = \frac { 1 } { x } - 1$$

Accepted Answer

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

Question 4

Find the function value.
-For $f ( x ) = - | x - 2 |$, find $f ( - 4 )$.

Accepted Answer

A)  $- 4$ 
B)  2 
C)  $- 6$ 
D)  6 
A)  $- 4$ 
B)  2 
C)  $- 6$ 
D)  6

Question 5

Give the coordinates of the vertex and graph the equation in a window that includes the vertex.
-$y=-0.2 x^{2}-14 x+6$

Accepted Answer

A)  Vertex: $( - 35,251 )$
  
B)  Vertex: $( - 17.5,67.25 )$
  
C)  Vertex: $( 35,251 )$
  
D)  Vertex: $( 17.5,67.25 )$
  
A)  Vertex: $( - 35,251 )$
  
B)  Vertex: $( - 17.5,67.25 )$
  
C)  Vertex: $( 35,251 )$
  
D)  Vertex: $( 17.5,67.25 )$

Question 6

Use a graphing utility as an aid in factoring to
-$$22 x ^ { 2 } + 129 x + 44 = 0$$

Accepted Answer

A)  $x = \frac { 11 } { 2 } , x = - 4$ 
B)  $x = - 11 , x = - \frac { 4 } { 11 }$ 
C)  $x = - \frac { 11 } { 2 } , x = - \frac { 4 } { 11 }$ 
D)  $x = \frac { 11 } { 2 } , x = \frac { 4 } { 11 }$ 
A)  $x = \frac { 11 } { 2 } , x = - 4$ 
B)  $x = - 11 , x = - \frac { 4 } { 11 }$ 
C)  $x = - \frac { 11 } { 2 } , x = - \frac { 4 } { 11 }$ 
D)  $x = \frac { 11 } { 2 } , x = \frac { 4 } { 11 }$

Question 7

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal
places.
-$$2 n ^ { 2 } = - 12 n - 3$$

Accepted Answer

A)  $0.24 , - 6.24$ 
B)  $- 0.261 , - 5.739$ 
C)  $- 0.131 , - 2.869$ 
D)  $- 3.261 , - 8.739$ 
A)  $0.24 , - 6.24$ 
B)  $- 0.261 , - 5.739$ 
C)  $- 0.131 , - 2.869$ 
D)  $- 3.261 , - 8.739$

Question 8

John owns a hot dog stand. His profit, in dollars, is given by the equation $P ( x ) = P = - x ^ { 2 } + 14 x + 59$ , where x is the number of hot dogs sold. What is the most he can earn?

Accepted Answer

A)  $150 
B)  $108 
C)  $49 
D)  $87 
A)  $150 
B)  $108 
C)  $49 
D)  $87

Question 9

Sketch the complete graph of the function.
-$$f ( x ) = x ^ { 2 } + 200 x - 600$$

Accepted Answer

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

Question 10

Determine if the function is concave up or concave down in the first quadrant.
-$y = x ^ { 3 / 2 }$

Accepted Answer

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

Question 11

If an amount of money, called the principal, P, is deposited into an account that earns interest at a rate r, compounded annually, then in two years that investment will grow to an amount A, given by the formula $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { r } ) ^ { 2 }$ If a principal amount of $4500 grows to $5445.00 in two years, what is the interest rate?

Accepted Answer

A)  12% 
B)  10% 
C)  8% 
D)  11% 
A)  12% 
B)  10% 
C)  8% 
D)  11%

Question 12

Determine if the vertex of the graph is a maximum point or a minimum point.
-$y = x ^ { 2 } - 2 x + 1$

Accepted Answer

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

Question 13

Find a quadratic function that best fits the data. Give answers to the nearest hundredth.
-$\begin{array}{c|c|c|c}
\mathrm{x} & -10.2 & 1.4 & 7 \
\hline \mathrm{y} & 100 & 5 & 56
\end{array}$

Accepted Answer

A)  $\mathrm { y } = 0.09 + 8.33 \mathrm { x } - 6.85$ 
B)  $y = 0.53 x ^ { 2 } + 4.68 x - 2.5$ 
C)  $y = 1.01 x ^ { 2 } - 0.66 x + 2.11$ 
D)  $y = 1.01 x ^ { 2 } + 0.66 x + 2.11$ 
A)  $\mathrm { y } = 0.09 + 8.33 \mathrm { x } - 6.85$ 
B)  $y = 0.53 x ^ { 2 } + 4.68 x - 2.5$ 
C)  $y = 1.01 x ^ { 2 } - 0.66 x + 2.11$ 
D)  $y = 1.01 x ^ { 2 } + 0.66 x + 2.11$

Question 14

Your company uses the quadratic model y $y = - 4.5 x ^ { 2 } + 150 x$ 150x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new customers can you
Expect to gain in week 2?

Accepted Answer

A)  291 customers 
B)  141 customers 
C)  132 customers 
D)  282 customers 
A)  291 customers 
B)  141 customers 
C)  132 customers 
D)  282 customers

Question 15

Use factoring to solve the equation
-$$3 k ^ { 2 } - 11 k - 4 = 0$$

Accepted Answer

A)  $- \frac { 1 } { 3 } , 3$ 
B)  $- 3,4$ 
C)  $\frac { 1 } { 11 } , - \frac { 1 } { 3 }$ 
D)  $- \frac { 1 } { 3 } , 4$ 
A)  $- \frac { 1 } { 3 } , 3$ 
B)  $- 3,4$ 
C)  $\frac { 1 } { 11 } , - \frac { 1 } { 3 }$ 
D)  $- \frac { 1 } { 3 } , 4$

Question 16

Provide an appropriate response.
-Write the equation of the quadratic function whose graph is shown.

Accepted Answer

A)  $y = - ( x + 4 ) ^ { 2 } + 6$ 
B)  $y = - ( x - 4 ) ^ { 2 } + 6$ 
C)  $y = - 2 ( x - 4 ) ^ { 2 } + 6$ 
D)  $y = ( x - 4 ) ^ { 2 } + 6$ 
A)  $y = - ( x + 4 ) ^ { 2 } + 6$ 
B)  $y = - ( x - 4 ) ^ { 2 } + 6$ 
C)  $y = - 2 ( x - 4 ) ^ { 2 } + 6$ 
D)  $y = ( x - 4 ) ^ { 2 } + 6$

Question 17

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. Use quadratic regression to determine the profit in the fourth year.

Accepted Answer

A)  4.28 million 
B)  4.35 million 
C)  6.5 million 
D)  4.20 million 
A)  4.28 million 
B)  4.35 million 
C)  6.5 million 
D)  4.20 million

Question 18

If a ball is thrown upward at 64 feet per second from the top of a building that is 120 feet high, the height of the ball can be modeled by $\mathrm { S } = 120 + 64 \mathrm { t } - 16 \mathrm { t } ^ { 2 }$ feet, where t is the number of seconds after the ball is thrown. After
How many seconds does the ball reach its maximum height?

Accepted Answer

A)  2 sec 
B)  4 sec 
C)  1 sec 
D)  3.8 sec 
A)  2 sec 
B)  4 sec 
C)  1 sec 
D)  3.8 sec

Question 19

Use factoring to solve the equation
-$$x ^ { 2 } + 10 x = - 16$$

Accepted Answer

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

Question 20

Suppose that y varies directly as the $$3 / 2 \text { power of } x \text {, and that } y = 192 \text { when } x = 16 . \text { Find } y \text { when } x = 9$$ .

Accepted Answer

A)  81 
B)  48 
C)  3 
D)  192 
A)  81 
B)  48 
C)  3 
D)  192

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

If 5000 feet of fencing are used to enclose a rectangular field, the resulting area of the field is A=x(2500-x) , where x is the width of the pen. What is the maximum possible area of the pen?

Graph - $f ( x ) = \frac { 1 } { x } - 1$ $Graph - f ( x ) = \frac { 1 } { x } - 1$

Find the function value. -For $f ( x ) = - | x - 2 |$ , find $f ( - 4 )$ .

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=-0.2 x^{2}-14 x+6$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=-0.2 x^{2}-14 x+6$

Use a graphing utility as an aid in factoring to - $22 x ^ { 2 } + 129 x + 44 = 0$

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $2 n ^ { 2 } = - 12 n - 3$

John owns a hot dog stand. His profit, in dollars, is given by the equation $P ( x ) = P = - x ^ { 2 } + 14 x + 59$ , where x is the number of hot dogs sold. What is the most he can earn?

Sketch the complete graph of the function. - $f ( x ) = x ^ { 2 } + 200 x - 600$ $Sketch the complete graph of the function. - f ( x ) = x ^ { 2 } + 200 x - 600$

Determine if the function is concave up or concave down in the first quadrant. - $y = x ^ { 3 / 2 }$

Determine if the vertex of the graph is a maximum point or a minimum point. - $y = x ^ { 2 } - 2 x + 1$

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - -10.2 1.4 7 100 5 56

Your company uses the quadratic model y $y = - 4.5 x ^ { 2 } + 150 x$ 150x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new customers can you Expect to gain in week 2?

Use factoring to solve the equation - $3 k ^ { 2 } - 11 k - 4 = 0$

Provide an appropriate response. -Write the equation of the quadratic function whose graph is shown.

Use factoring to solve the equation - $x ^ { 2 } + 10 x = - 16$

Suppose that y varies directly as the $3 / 2 \text { power of } x \text {, and that } y = 192 \text { when } x = 16 . \text { Find } y \text { when } x = 9$ .

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

Determine if the graph of the function is concave up or concave down - y=(x+2)2y = ( x + 2 ) ^ { 2 }y=(x+2)2

If 5000 feet of fencing are used to enclose a rectangular field, the resulting area of the field is A=x(2500-x) , where x is the width of the pen. What is the maximum possible area of the pen?

Graph - f(x)=1x−1f ( x ) = \frac { 1 } { x } - 1f(x)=x1​−1

Find the function value. -For f(x)=−∣x−2∣f ( x ) = - | x - 2 |f(x)=−∣x−2∣ , find f(−4)f ( - 4 )f(−4) .

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=−0.2x2−14x+6y=-0.2 x^{2}-14 x+6y=−0.2x2−14x+6

Use a graphing utility as an aid in factoring to - 22x2+129x+44=022 x ^ { 2 } + 129 x + 44 = 022x2+129x+44=0

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - 2n2=−12n−32 n ^ { 2 } = - 12 n - 32n2=−12n−3

John owns a hot dog stand. His profit, in dollars, is given by the equation P(x)=P=−x2+14x+59P ( x ) = P = - x ^ { 2 } + 14 x + 59P(x)=P=−x2+14x+59 , where x is the number of hot dogs sold. What is the most he can earn?

Sketch the complete graph of the function. - f(x)=x2+200x−600f ( x ) = x ^ { 2 } + 200 x - 600f(x)=x2+200x−600

Determine if the function is concave up or concave down in the first quadrant. - y=x3/2y = x ^ { 3 / 2 }y=x3/2

Determine if the vertex of the graph is a maximum point or a minimum point. - y=x2−2x+1y = x ^ { 2 } - 2 x + 1y=x2−2x+1

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - -10.2 1.4 7 100 5 56

Your company uses the quadratic model y y=−4.5x2+150xy = - 4.5 x ^ { 2 } + 150 xy=−4.5x2+150x 150x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new customers can you Expect to gain in week 2?

Use factoring to solve the equation - 3k2−11k−4=03 k ^ { 2 } - 11 k - 4 = 03k2−11k−4=0

Provide an appropriate response. -Write the equation of the quadratic function whose graph is shown.

Use factoring to solve the equation - x2+10x=−16x ^ { 2 } + 10 x = - 16x2+10x=−16

Suppose that y varies directly as the 3/2 power of x, and that y=192 when x=16. Find y when x=93 / 2 \text { power of } x \text {, and that } y = 192 \text { when } x = 16 . \text { Find } y \text { when } x = 93/2 power of x, and that y=192 when x=16. Find y when x=9 .

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

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

Graph - $f ( x ) = \frac { 1 } { x } - 1$ $Graph - f ( x ) = \frac { 1 } { x } - 1$

Find the function value. -For $f ( x ) = - | x - 2 |$ , find $f ( - 4 )$ .

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y=-0.2 x^{2}-14 x+6$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=-0.2 x^{2}-14 x+6$

Use a graphing utility as an aid in factoring to - $22 x ^ { 2 } + 129 x + 44 = 0$

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $2 n ^ { 2 } = - 12 n - 3$

John owns a hot dog stand. His profit, in dollars, is given by the equation $P ( x ) = P = - x ^ { 2 } + 14 x + 59$ , where x is the number of hot dogs sold. What is the most he can earn?

Sketch the complete graph of the function. - $f ( x ) = x ^ { 2 } + 200 x - 600$ $Sketch the complete graph of the function. - f ( x ) = x ^ { 2 } + 200 x - 600$

Determine if the function is concave up or concave down in the first quadrant. - $y = x ^ { 3 / 2 }$

Determine if the vertex of the graph is a maximum point or a minimum point. - $y = x ^ { 2 } - 2 x + 1$

Your company uses the quadratic model y $y = - 4.5 x ^ { 2 } + 150 x$ 150x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new customers can you Expect to gain in week 2?

Use factoring to solve the equation - $3 k ^ { 2 } - 11 k - 4 = 0$

Use factoring to solve the equation - $x ^ { 2 } + 10 x = - 16$

Suppose that y varies directly as the $3 / 2 \text { power of } x \text {, and that } y = 192 \text { when } x = 16 . \text { Find } y \text { when } x = 9$ .