Question 1

Graph the given function.? $f ( x ) = 2 -$ $x ^ { 2 }$ ?

Accepted Answer

A)    ? 
B)    ? 
C)    ? 
D)    ? 
E)    ? 
A)    ? 
B)    ? 
C)    ? 
D)    ? 
E)    ? D

Question 2

The total revenue R earned per day (in dollars)from a pet-sitting service is given by? $R ( p ) = - 12 p ^ { 2 } + 150 p$ ? where p is the price charged per pet (in dollars).
?
Find the revenue when the price per pet is $3.
?

Accepted Answer

A) $372.00 
B) $352.00 
C) $382.00 
D) $362.00 
E) $342.00 
A) $372.00 
B) $352.00 
C) $382.00 
D) $362.00 
E) $342.00 E

Question 3

Write the quadratic function $f ( x ) = - x ^ { 2 } + 8 x - 8$ in standard form.

Accepted Answer

A)  $f ( x ) = ( x - 8 ) ^ { 2 } - 4$ 
B)  $f ( x ) = ( x - 4 ) ^ { 2 } - 8$ 
C)  $f ( x ) = - ( x + 4 ) ^ { 2 } + 8$ 
D)  $f ( x ) = - ( x + 8 ) ^ { 2 } - 4$ 
E)  $f ( x ) = - ( x - 4 ) ^ { 2 } + 8$ 
A)  $f ( x ) = ( x - 8 ) ^ { 2 } - 4$ 
B)  $f ( x ) = ( x - 4 ) ^ { 2 } - 8$ 
C)  $f ( x ) = - ( x + 4 ) ^ { 2 } + 8$ 
D)  $f ( x ) = - ( x + 8 ) ^ { 2 } - 4$ 
E)  $f ( x ) = - ( x - 4 ) ^ { 2 } + 8$ E

Question 4

Select the graph of the function $y = x ^ { 2 } - 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

Accepted Answer

A)    Vertical shift. 
B)    Vertical shift. 
C)    Vertical shift. 
D)    Vertical shift. 
E) ?   Vertical shift. 
A)    Vertical shift. 
B)    Vertical shift. 
C)    Vertical shift. 
D)    Vertical shift. 
E) ?   Vertical shift.

Question 5

Find the vertex of the parabola. y = x2 - 12x + 36

Accepted Answer

A) (6,0) 
B) (0,6) 
C) (-24,0) 
D) (36,0) 
E) (6,-24) 
A) (6,0) 
B) (0,6) 
C) (-24,0) 
D) (36,0) 
E) (6,-24)

Question 6

A manufacturer of lighting fixtures has daily production costs of $C = 800 - 80 x + 0.25 x ^ { 2 }$ where C is the total cost (in dollars)and x is the number of units produced.How many fixtures should be produced each day to yield a minimum cost? (Round your answer to two decimal places. )
?

Accepted Answer

A) 160 
B) 106.67 
C) 320 
D) 400 
E) 800 ? 
A) 160 
B) 106.67 
C) 320 
D) 400 
E) 800 ?

Question 7

Find the standard form of the quadratic function shown below:?   ?

Accepted Answer

A)  $f ( x ) = ( x + 2 ) ^ { 2 } - 3$ 
B)  $f ( x ) =$ $\frac { 1 } { 2 }$ $( x - 2 ) ^ { 2 } + 3$ 
C)  $f ( x ) = -$ $\frac { 2 } { 3 }$ $( x - 1 ) ^ { 2 } + 3$ 
D)  $f ( x ) =$ $\frac { 1 } { 2 }$ $( x + 2 ) ^ { 2 } - 3$ 
E)  $f ( x ) =$ $\frac { 1 } { 4 }$ $( x - 2 ) ^ { 2 } + 3$ 
A)  $f ( x ) = ( x + 2 ) ^ { 2 } - 3$ 
B)  $f ( x ) =$ $\frac { 1 } { 2 }$ $( x - 2 ) ^ { 2 } + 3$ 
C)  $f ( x ) = -$ $\frac { 2 } { 3 }$ $( x - 1 ) ^ { 2 } + 3$ 
D)  $f ( x ) =$ $\frac { 1 } { 2 }$ $( x + 2 ) ^ { 2 } - 3$ 
E)  $f ( x ) =$ $\frac { 1 } { 4 }$ $( x - 2 ) ^ { 2 } + 3$

Question 8

From the graph of the quadratic function $f ( x ) = ( x + 6 ) ^ { 2 } - 1$ ,determine the equation of the axis of symmetry.

Accepted Answer

A)  $x = - 6$ 
B)  $x = - 1$ 
C)  $x = - \frac { 1 } { 6 }$ 
D)  $x = 1$ 
E)  $$x = 6$$ 
A)  $x = - 6$ 
B)  $x = - 1$ 
C)  $x = - \frac { 1 } { 6 }$ 
D)  $x = 1$ 
E)  $$x = 6$$

Question 9

A small theater has a seating capacity of 2000.When the ticket price is $20,attendance is 1500.For each $1 decrease in price,attendance increases by 50.The revenue R of the theater as a function of ticket price x is as follows $R ( x ) = - 50 x ^ { 2 } + 2500 x , 10 \leq x \leq 20$ What ticket price will yield a maximum revenue?

Accepted Answer

A) $55.00 ? 
B) $35.00 ? 
C) $25.00 ? 
D) $45.00 ? 
E) $65.00 ? 
A) $55.00 ? 
B) $35.00 ? 
C) $25.00 ? 
D) $45.00 ? 
E) $65.00 ?

Question 10

Select the graph of the function $y = \frac { 3 } { 2 } x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

Accepted Answer

A) ?   Vertical shrink. 
B)    ?Vertical stretch. 
C)    ?
?
Vertical stretch and reflection in the x-axis. 
D)    ?
?
Vertical shrink. 
E) ?   ?
?
Vertical stretch and reflection in the x-axis. 
A) ?   Vertical shrink. 
B)    ?Vertical stretch. 
C)    ?
?
Vertical stretch and reflection in the x-axis. 
D)    ?
?
Vertical shrink. 
E) ?   ?
?
Vertical stretch and reflection in the x-axis.

Question 11

Find the values of b such that the function $f ( x ) = x ^ { 2 } + b x - 25$ has the given minimum value -74. ?

Accepted Answer

A) ±16 
B) ±22 
C) ±14 
D) ±18 
E) ±20 
A) ±16 
B) ±22 
C) ±14 
D) ±18 
E) ±20

Question 12

Select the graph of the quadratic function $f ( x ) = ( x + 4 ) ^ { 2 } + 3$ .Identify the vertex and axis of symmetry. ?
?

Accepted Answer

A) ?   ?
Vertex: (-4,5)
Axis of symmetry: x = -4 
B) ?   ?
Vertex: (-4,1)
Axis of symmetry: x = -4 
C) ?   ?
Vertex: (-4,2)
Axis of symmetry: x = -4 
D)    ?
Vertex: (-4,4)
Axis of symmetry: x = -4 
E) ?   Vertex: (-4,3)
Axis of symmetry: x = -4 
A) ?   ?
Vertex: (-4,5)
Axis of symmetry: x = -4 
B) ?   ?
Vertex: (-4,1)
Axis of symmetry: x = -4 
C) ?   ?
Vertex: (-4,2)
Axis of symmetry: x = -4 
D)    ?
Vertex: (-4,4)
Axis of symmetry: x = -4 
E) ?   Vertex: (-4,3)
Axis of symmetry: x = -4

Question 13

Select the graph of the function $y = - 6 x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

Accepted Answer

A)    ?
Vertical stretch 
B)    ?
Vertical stretch and reflection in x-axis 
C)    ?
?
Reflection in x-axis 
D)    ?
?
Vertical shrink and reflection in x-axis 
E)    ?
?
Vertical shrink 
A)    ?
Vertical stretch 
B)    ?
Vertical stretch and reflection in x-axis 
C)    ?
?
Reflection in x-axis 
D)    ?
?
Vertical shrink and reflection in x-axis 
E)    ?
?
Vertical shrink

Question 14

Write the quadratic function $f ( x ) = \frac { 1 } { 4 } \left( x ^ { 2 } + 8 x - 20 \right)$ in standard form.

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 4 } ( x + 4 ) ^ { 2 } - 9$ 
B)  $f ( x ) = \frac { 1 } { 4 } ( x - 9 ) ^ { 2 } + 4$ 
C)  $f ( x ) = \frac { 1 } { 4 } ( x - 4 ) ^ { 2 } + 9$ 
D)  $f ( x ) = - \frac { 1 } { 9 } ( x + 4 ) ^ { 2 } - 9$ 
E)  $f ( x ) = - \frac { 1 } { 9 } ( x - 4 ) ^ { 2 } - 9$ 
A)  $f ( x ) = \frac { 1 } { 4 } ( x + 4 ) ^ { 2 } - 9$ 
B)  $f ( x ) = \frac { 1 } { 4 } ( x - 9 ) ^ { 2 } + 4$ 
C)  $f ( x ) = \frac { 1 } { 4 } ( x - 4 ) ^ { 2 } + 9$ 
D)  $f ( x ) = - \frac { 1 } { 9 } ( x + 4 ) ^ { 2 } - 9$ 
E)  $f ( x ) = - \frac { 1 } { 9 } ( x - 4 ) ^ { 2 } - 9$

Question 15

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$ .Identify the vertex and axis of symmetry. ?

Accepted Answer

A) ?   ?
?
Vertex: (0,1)
Axis of symmetry: y-axis 
B)    ?
?
Vertex: (0,3)
Axis of symmetry: y-axis 
C)    ?
?
Vertex: (0,4)
Axis of symmetry: y-axis 
D)    ?
Vertex: (0,5)
Axis of symmetry: y-axis
? 
E) ?   ?
Vertex: (0,2)
Axis of symmetry: y-axis 
A) ?   ?
?
Vertex: (0,1)
Axis of symmetry: y-axis 
B)    ?
?
Vertex: (0,3)
Axis of symmetry: y-axis 
C)    ?
?
Vertex: (0,4)
Axis of symmetry: y-axis 
D)    ?
Vertex: (0,5)
Axis of symmetry: y-axis
? 
E) ?   ?
Vertex: (0,2)
Axis of symmetry: y-axis

Question 16

Find two positive real numbers whose product is a maximum and whose sum is 160.

Accepted Answer

A)  $89,71$ 
B)  $85,75$ 
C)  $80,80$ 
D)  $78,82$ 
E)  $92,68$ 
A)  $89,71$ 
B)  $85,75$ 
C)  $80,80$ 
D)  $78,82$ 
E)  $92,68$

Question 17

The total revenue R earned (in thousands of dollars)from manufacturing handheld video games is given by? $R ( p ) = - 25 p ^ { 2 } + 1900 p$ ? where p is the price per unit (in dollars).
?
Find the unit price that will yield a maximum revenue.
?

Accepted Answer

A) $42.00 
B) $40.00 
C) $41.00 
D) $39.00 
E) $38.00 
A) $42.00 
B) $40.00 
C) $41.00 
D) $39.00 
E) $38.00

Question 18

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .Identify the axis of symmetry. ?

Accepted Answer

A)    Axis of symmetry: x = -1 
B)    ?Axis of symmetry: x = -1 
C)    Axis of symmetry: x = -1 
D)    ?Axis of symmetry: x = -1 
E)    Axis of symmetry: x = -1 
A)    Axis of symmetry: x = -1 
B)    ?Axis of symmetry: x = -1 
C)    Axis of symmetry: x = -1 
D)    ?Axis of symmetry: x = -1 
E)    Axis of symmetry: x = -1

Question 19

Find two positive real numbers whose product is a maximum.The sum is 140. ​

Accepted Answer

A) 90,50 
B) ​100,40 
C) ​70,​70 
D) ​80,60 
E) ​10,130 
A) 90,50 
B) ​100,40 
C) ​70,​70 
D) ​80,60 
E) ​10,130

Question 20

Graph the quadratic function.? $$f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } - 2$$ ?

Accepted Answer

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

Exam 11: Quadratic Functions and Models

Graph the given function.? f(x)=2−f ( x ) = 2 -f(x)=2− x2x ^ { 2 }x2 ?

The total revenue R earned per day (in dollars)from a pet-sitting service is given by? R(p)=−12p2+150pR ( p ) = - 12 p ^ { 2 } + 150 pR(p)=−12p2+150p ? where p is the price charged per pet (in dollars). ? Find the revenue when the price per pet is $3. ?

Write the quadratic function f(x)=−x2+8x−8f ( x ) = - x ^ { 2 } + 8 x - 8f(x)=−x2+8x−8 in standard form.

Select the graph of the function y=x2−1y = x ^ { 2 } - 1y=x2−1 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 . ?

Find the vertex of the parabola. y = x2 - 12x + 36

Find the standard form of the quadratic function shown below:? ?

From the graph of the quadratic function f(x)=(x+6)2−1f ( x ) = ( x + 6 ) ^ { 2 } - 1f(x)=(x+6)2−1 ,determine the equation of the axis of symmetry.

Select the graph of the function y=32x2y = \frac { 3 } { 2 } x ^ { 2 }y=23​x2 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 . ?

Find the values of b such that the function f(x)=x2+bx−25f ( x ) = x ^ { 2 } + b x - 25f(x)=x2+bx−25 has the given minimum value -74. ?

Select the graph of the quadratic function f(x)=(x+4)2+3f ( x ) = ( x + 4 ) ^ { 2 } + 3f(x)=(x+4)2+3 .Identify the vertex and axis of symmetry. ? ?

Select the graph of the function y=−6x2y = - 6 x ^ { 2 }y=−6x2 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 . ?

Write the quadratic function f(x)=14(x2+8x−20)f ( x ) = \frac { 1 } { 4 } \left( x ^ { 2 } + 8 x - 20 \right)f(x)=41​(x2+8x−20) in standard form.

Select the graph of the quadratic function f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5 .Identify the vertex and axis of symmetry. ?

Find two positive real numbers whose product is a maximum and whose sum is 160.

The total revenue R earned (in thousands of dollars)from manufacturing handheld video games is given by? R(p)=−25p2+1900pR ( p ) = - 25 p ^ { 2 } + 1900 pR(p)=−25p2+1900p ? where p is the price per unit (in dollars). ? Find the unit price that will yield a maximum revenue. ?

Select the graph of the quadratic function f(x)=x2+2x+2f ( x ) = x ^ { 2 } + 2 x + 2f(x)=x2+2x+2 .Identify the axis of symmetry. ?

Find two positive real numbers whose product is a maximum.The sum is 140. ​

Graph the quadratic function.? f(x)=−13x2−2f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } - 2f(x)=−31​x2−2 ?

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Graph the given function.? $f ( x ) = 2 -$ $x ^ { 2 }$ ? $Graph the given function.? f ( x ) = 2 - x ^ { 2 } ?$

The total revenue R earned per day (in dollars)from a pet-sitting service is given by? $R ( p ) = - 12 p ^ { 2 } + 150 p$ ? where p is the price charged per pet (in dollars). ? Find the revenue when the price per pet is $3. ?

Write the quadratic function $f ( x ) = - x ^ { 2 } + 8 x - 8$ in standard form.

Select the graph of the function $y = x ^ { 2 } - 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

Find the vertex of the parabola. y = x² - 12x + 36

From the graph of the quadratic function $f ( x ) = ( x + 6 ) ^ { 2 } - 1$ ,determine the equation of the axis of symmetry.

Select the graph of the function $y = \frac { 3 } { 2 } x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

Find the values of b such that the function $f ( x ) = x ^ { 2 } + b x - 25$ has the given minimum value -74. ?

Select the graph of the quadratic function $f ( x ) = ( x + 4 ) ^ { 2 } + 3$ .Identify the vertex and axis of symmetry. ? ?

Select the graph of the function $y = - 6 x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

Write the quadratic function $f ( x ) = \frac { 1 } { 4 } \left( x ^ { 2 } + 8 x - 20 \right)$ in standard form.

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$ .Identify the vertex and axis of symmetry. ?

The total revenue R earned (in thousands of dollars)from manufacturing handheld video games is given by? $R ( p ) = - 25 p ^ { 2 } + 1900 p$ ? where p is the price per unit (in dollars). ? Find the unit price that will yield a maximum revenue. ?

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .Identify the axis of symmetry. ?

Find two positive real numbers whose product is a maximum.The sum is 140.

Graph the quadratic function.? $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } - 2$ ?