Question 1

Select the graph of the function $y = ( 3 x ) ^ { 2 } - 5$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

Accepted Answer

A)    ?
?
Horizontal shrink and vertical shift. 
B)    ?
?
Horizontal shrink and vertical shift. 
C)    ?
?
Horizontal shrink and vertical shift. 
D)    ?
?
Horizontal shrink and vertical shift. 
E) ?   ?
?
Horizontal shrink and vertical shift. 
A)    ?
?
Horizontal shrink and vertical shift. 
B)    ?
?
Horizontal shrink and vertical shift. 
C)    ?
?
Horizontal shrink and vertical shift. 
D)    ?
?
Horizontal shrink and vertical shift. 
E) ?   ?
?
Horizontal shrink and vertical shift.

Question 2

Find two positive real numbers whose product is a maximum. ​
The sum of the first and twice the second is 56.
(Round your answer to two decimal places. )
​

Accepted Answer

A) 28,5.6 
B) 28,9.33​ 
C) 28,7 
D) 28,14 
E) 14,14 
A) 28,5.6 
B) 28,9.33​ 
C) 28,7 
D) 28,14 
E) 14,14

Question 3

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

Accepted Answer

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

Question 4

Determine the x-intercept(s)of the quadratic function $$f ( x ) = x ^ { 2 } + 2 x + 2$$ .

Accepted Answer

A)  $( 0,0 ) , ( - 5,0 )$ 
B)  $( - 7,0 ) , ( - 4,0 )$ 
C) no x-intercept(s) 
D)  $( - 7,0 ) , ( - 5,0 )$ 
E)  $( - 2,0 ) , ( 2,0 )$ 
A)  $( 0,0 ) , ( - 5,0 )$ 
B)  $( - 7,0 ) , ( - 4,0 )$ 
C) no x-intercept(s) 
D)  $( - 7,0 ) , ( - 5,0 )$ 
E)  $( - 2,0 ) , ( 2,0 )$

Question 5

From the graph of the quadratic function $f ( x ) = - x ^ { 2 } + 12 x + 4$ ,determine the equation of the axis of symmetry.

Accepted Answer

A)  $x = 6$ 
B)  $x = 4$ 
C)  $x = 40$ 
D)  $x = - 12$ 
E)  $x = - 32$ 
A)  $x = 6$ 
B)  $x = 4$ 
C)  $x = 40$ 
D)  $x = - 12$ 
E)  $x = - 32$

Question 6

Find the vertex of the parabola. ​
Y = 3x2 - 1
​

Accepted Answer

A) (-1,3) 
B) (0,-1) 
C) (3,-1) 
D) (-1,0) 
E) (0,3) 
A) (-1,3) 
B) (0,-1) 
C) (3,-1) 
D) (-1,0) 
E) (0,3)

Question 7

Find the values of b such that the function $f ( x ) = x ^ { 2 } + b x + 59$ has the given minimum value 10. ?

Accepted Answer

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

Question 8

Determine the x-intercept(s)of the quadratic function $f ( x ) = x ^ { 2 } + 8 x + 12$ .

Accepted Answer

A)  $( 2,0 ) , ( 6,0 )$ 
B)  $( 6,0 ) , ( 5,0 )$ 
C)  $( - 2,0 ) , ( - 6,0 )$ 
D)  $( - 6,0 ) , ( - 5,0 )$ 
E) no x-intercept(s) 
A)  $( 2,0 ) , ( 6,0 )$ 
B)  $( 6,0 ) , ( 5,0 )$ 
C)  $( - 2,0 ) , ( - 6,0 )$ 
D)  $( - 6,0 ) , ( - 5,0 )$ 
E) no x-intercept(s)

Question 9

Find two positive real numbers whose product is a maximum. ​
The sum of the first and three times the second is 48.
​

Accepted Answer

A) 24,8 
B) 24,16 
C) 16,4 
D) 24,6 
E) 42,6 
A) 24,8 
B) 24,16 
C) 16,4 
D) 24,6 
E) 42,6

Question 10

Graph the quadratic function. ​
F (x)= - x2 - 4x + 1
​

Accepted Answer

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

Question 11

Compare the graph of $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ with $n ( x ) = x ^ { 2 }$ .

Accepted Answer

A)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units,shifts downward 6 units,and stretches by a factor of 7. 
B)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units,shifts upward 6 units,and stretches by a factor of 7. 
C)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts downward 6 units,and shrinks by a factor of $\frac { 1 } { 7 }$ . 
D)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts upward 6 units,and shrinks by a factor of $\frac { 1 } { 7 }$ . 
E)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts upward 6 units,and stretches by a factor of 7. 
A)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units,shifts downward 6 units,and stretches by a factor of 7. 
B)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units,shifts upward 6 units,and stretches by a factor of 7. 
C)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts downward 6 units,and shrinks by a factor of $\frac { 1 } { 7 }$ . 
D)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts upward 6 units,and shrinks by a factor of $\frac { 1 } { 7 }$ . 
E)  $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts upward 6 units,and stretches by a factor of 7.

Question 12

Find the vertex of the parabola.
​
y = x2 + 14x + 49
​
Please enter your ANS. as an ordered pair.

Accepted Answer

Question 13

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

Accepted Answer

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

Question 14

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .

Accepted Answer

A)  $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$ 
B)  $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$ 
C)  $\left( - \frac { 5 } { 2 } , 1 \right)$ ? 
D)  $\left( - \frac { 5 } { 2 } , \frac { 27 } { 2 } \right)$ 
E)  $\left( 5 , \frac { 29 } { 4 } \right)$ 
A)  $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$ 
B)  $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$ 
C)  $\left( - \frac { 5 } { 2 } , 1 \right)$ ? 
D)  $\left( - \frac { 5 } { 2 } , \frac { 27 } { 2 } \right)$ 
E)  $\left( 5 , \frac { 29 } { 4 } \right)$

Question 15

The height,h(x),of a punted rugby ball is given by $h ( x ) = - \frac { 1 } { 64 } x ^ { 2 } + \frac { 21 } { 32 } x + 3$ where x is the horizontal distance in feet from the point where the ball is punted.How far,horizontally,is the ball from the kicker when it is at its highest point?

Accepted Answer

A)  $45 \text { feet }$ 
B)  $21 \text { feet }$ 
C)  $26 \text { feet }$ 
D)  $31 \text { feet }$ 
E)  $24 \text { feet }$ 
A)  $45 \text { feet }$ 
B)  $21 \text { feet }$ 
C)  $26 \text { feet }$ 
D)  $31 \text { feet }$ 
E)  $24 \text { feet }$

Question 16

The function $f ( x ) = x ^ { 2 } - 5$ is one-to-one on the domain $$( x \leq 0 )$$ .Find $f ^ { - 1 } ( x )$ . ?

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 5$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x + 5 }$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt { x + 5 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$ 
A)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 5$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x + 5 }$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt { x + 5 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$

Question 17

The total revenue R earned per day (in dollars)from a pet-sitting service is given by? $R ( p ) = - 10 p ^ { 2 } + 120 p$ ? where p is the price charged per pet (in dollars).
?
Find the price that will yield a maximum revenue.
?

Accepted Answer

A) $7.00 
B) $10.00 
C) $8.00 
D) $6.00 
E) $9.00 
A) $7.00 
B) $10.00 
C) $8.00 
D) $6.00 
E) $9.00

Question 18

Find the values of b such that the function $f ( x ) = - x ^ { 2 } + b x - 16$ has the given maximum value 65. ?

Accepted Answer

A) ±18 
B) ±22 
C) ±24 
D) ±20 
E) ±26 
A) ±18 
B) ±22 
C) ±24 
D) ±20 
E) ±26

Question 19

Find the vertex of the parabola. y = - x2 + 16x - 60

Accepted Answer

A) (-8,4) 
B) (8,4) 
C) (-8,-4) 
D) (8,-30) 
E) (4,8) 
A) (-8,4) 
B) (8,4) 
C) (-8,-4) 
D) (8,-30) 
E) (4,8)

Question 20

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 125.Write the revenue R of the theater as a function of ticket price x. ?

Accepted Answer

A)  $R ( x ) = 125 x ^ { 2 } + 3000 x , 16 \leq x \leq 20$ 
B)  $R ( x ) = - 125 x ^ { 2 } + 1000 x , 16 \leq x \leq 20$ 
C)  $R ( x ) = - 125 x ^ { 3 } + 500 x , 16 \leq x \leq 20$ 
D)  $R ( x ) = - 125 x ^ { 2 } - 350 x , 16 \leq x \leq 20$ 
E)  $R ( x ) = - 125 x ^ { 2 } + 4000 x , 16 \leq x \leq 20$ 
A)  $R ( x ) = 125 x ^ { 2 } + 3000 x , 16 \leq x \leq 20$ 
B)  $R ( x ) = - 125 x ^ { 2 } + 1000 x , 16 \leq x \leq 20$ 
C)  $R ( x ) = - 125 x ^ { 3 } + 500 x , 16 \leq x \leq 20$ 
D)  $R ( x ) = - 125 x ^ { 2 } - 350 x , 16 \leq x \leq 20$ 
E)  $R ( x ) = - 125 x ^ { 2 } + 4000 x , 16 \leq x \leq 20$

Exam 11: Quadratic Functions and Models

Select the graph of the function y=(3x)2−5y = ( 3 x ) ^ { 2 } - 5y=(3x)2−5 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 . ?

Find two positive real numbers whose product is a maximum. ​ The sum of the first and twice the second is 56. (Round your answer to two decimal places. ) ​

Select the graph of the quadratic function f(x)=3−x2f ( x ) = 3 - x ^ { 2 }f(x)=3−x2 .Identify the vertex and axis of symmetry. ?

Determine the x-intercept(s)of the quadratic function f(x)=x2+2x+2f ( x ) = x ^ { 2 } + 2 x + 2f(x)=x2+2x+2 .

From the graph of the quadratic function f(x)=−x2+12x+4f ( x ) = - x ^ { 2 } + 12 x + 4f(x)=−x2+12x+4 ,determine the equation of the axis of symmetry.

Find the vertex of the parabola. ​ Y = 3x2 - 1 ​

Find the values of b such that the function f(x)=x2+bx+59f ( x ) = x ^ { 2 } + b x + 59f(x)=x2+bx+59 has the given minimum value 10. ?

Determine the x-intercept(s)of the quadratic function f(x)=x2+8x+12f ( x ) = x ^ { 2 } + 8 x + 12f(x)=x2+8x+12 .

Find two positive real numbers whose product is a maximum. ​ The sum of the first and three times the second is 48. ​

Graph the quadratic function. ​ F (x)= - x2 - 4x + 1 ​

Compare the graph of n(x)=7(x−3)2+6n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6n(x)=7(x−3)2+6 with n(x)=x2n ( x ) = x ^ { 2 }n(x)=x2 .

Find the vertex of the parabola. ​ y = x2 + 14x + 49 ​ Please enter your ANS. as an ordered pair.

Select the graph of the quadratic function f(x)=x2−3f ( x ) = x ^ { 2 } - 3f(x)=x2−3 .Identify the vertex and axis of symmetry. ?

Determine the vertex of the graph of the quadratic function f(x)=x2+5x+294f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }f(x)=x2+5x+429​ .

The function f(x)=x2−5f ( x ) = x ^ { 2 } - 5f(x)=x2−5 is one-to-one on the domain (x≤0)( x \leq 0 )(x≤0) .Find f−1(x)f ^ { - 1 } ( x )f−1(x) . ?

The total revenue R earned per day (in dollars)from a pet-sitting service is given by? R(p)=−10p2+120pR ( p ) = - 10 p ^ { 2 } + 120 pR(p)=−10p2+120p ? where p is the price charged per pet (in dollars). ? Find the price that will yield a maximum revenue. ?

Find the values of b such that the function f(x)=−x2+bx−16f ( x ) = - x ^ { 2 } + b x - 16f(x)=−x2+bx−16 has the given maximum value 65. ?

Find the vertex of the parabola. y = - x2 + 16x - 60

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 125.Write the revenue R of the theater as a function of ticket price x. ?

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

Select the graph of the function $y = ( 3 x ) ^ { 2 } - 5$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

Find two positive real numbers whose product is a maximum. The sum of the first and twice the second is 56. (Round your answer to two decimal places. )

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

Determine the x-intercept(s)of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .

From the graph of the quadratic function $f ( x ) = - x ^ { 2 } + 12 x + 4$ ,determine the equation of the axis of symmetry.

Find the vertex of the parabola. Y = 3x² - 1

Find the values of b such that the function $f ( x ) = x ^ { 2 } + b x + 59$ has the given minimum value 10. ?

Determine the x-intercept(s)of the quadratic function $f ( x ) = x ^ { 2 } + 8 x + 12$ .

Find two positive real numbers whose product is a maximum. The sum of the first and three times the second is 48.

Graph the quadratic function. F (x)= - x² - 4x + 1

Compare the graph of $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ with $n ( x ) = x ^ { 2 }$ .

Find the vertex of the parabola. y = x² + 14x + 49 Please enter your ANS. as an ordered pair.

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

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .

The function $f ( x ) = x ^ { 2 } - 5$ is one-to-one on the domain $( x \leq 0 )$ .Find $f ^ { - 1 } ( x )$ . ?

The total revenue R earned per day (in dollars)from a pet-sitting service is given by? $R ( p ) = - 10 p ^ { 2 } + 120 p$ ? where p is the price charged per pet (in dollars). ? Find the price that will yield a maximum revenue. ?

Find the values of b such that the function $f ( x ) = - x ^ { 2 } + b x - 16$ has the given maximum value 65. ?

Find the vertex of the parabola. y = - x² + 16x - 60