Exam 11: Quadratic Functions and Models

Write the standard form of the equation of the parabola that has a vertex at $\left( - \frac { 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 2,3 )$ .

(Multiple Choice)

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Question 41

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

(Multiple Choice)

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Question 42

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

(Multiple Choice)

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Question 43

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below.If the perimeter of the window is 40 ft,express the area,A,as a function of the width,x,of the window.

(Multiple Choice)

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Question 44

The total revenue R earned (in thousands of dollars)from manufacturing handheld video games is given by? $R ( p ) = - 25 p ^ { 2 } + 1200 p$ ? where p is the price per unit (in dollars). ? Find the revenue when the price per unit is $20. ?

(Multiple Choice)

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Question 45

Find the inverse of the one-to-one function.? $y = 7 x + 5$ ?

(Multiple Choice)

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Question 46

A farmer has 216 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.

(Multiple Choice)

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Question 47

Select the graph of the quadratic function.? $f ( x ) = x ^ { 2 } - 5 x$ ?

(Multiple Choice)

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Question 48

?Write the standard form of the equation of the parabola that has a vertex at (-6,-5)and passes through the point (-8,6). ?

(Multiple Choice)

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Question 49

Select the graph of the function $y = x ^ { 2 } + 4$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

(Multiple Choice)

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Question 50

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 160.

(Multiple Choice)

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Question 51

Select the graph of the function $y = ( x - 4 ) ^ { 2 } + 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

(Multiple Choice)

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Question 52

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

(Multiple Choice)

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Question 53

Compare the graph of $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ with $n ( x ) = x ^ { 2 }$ .

(Multiple Choice)

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Question 54

Graph the quadratic function. F (x)= x² + 2x

(Multiple Choice)

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Question 55

Find the vertex of the parabolic graph of the equation. y = 4(x - 5)² + 7

(Multiple Choice)

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Question 56

Graph the quadratic function. F (x)= - 4x² + 2

(Multiple Choice)

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Question 57

The profit P (in hundreds of dollars)that a company makes depends on the amount x (in hundreds of dollars)the company spends on advertising according to the model? $P = 230 + 30 x - 0.5 x ^ { 2 }$ ? What expenditure for advertising will yield a maximum profit? ?

(Multiple Choice)

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Question 58

The height y (in feet)of a punted football is given by? $y = - \frac { 20 } { 2025 } x ^ { 2 } + \frac { 9 } { 5 } x + 1.6$ ? where x is the horizontal distance (in feet)from the point at which the ball is punted. What is the maximum height of the punt? (Round your answer to two decimal places. ) ?

(Multiple Choice)

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Question 59

Write the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 5$ in standard form.

(Multiple Choice)

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Question 60

Exam 11: Quadratic Functions and Models

Write the standard form of the equation of the parabola that has a vertex at (−23,19)\left( - \frac { 2 } { 3 } , \frac { 1 } { 9 } \right)(−32​,91​) and passes through the point (2,3)( 2,3 )(2,3) .

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

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

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below.If the perimeter of the window is 40 ft,express the area,A,as a function of the width,x,of the window.

The total revenue R earned (in thousands of dollars)from manufacturing handheld video games is given by? R(p)=−25p2+1200pR ( p ) = - 25 p ^ { 2 } + 1200 pR(p)=−25p2+1200p ? where p is the price per unit (in dollars). ? Find the revenue when the price per unit is $20. ?

Find the inverse of the one-to-one function.? y=7x+5y = 7 x + 5y=7x+5 ?

A farmer has 216 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.

Select the graph of the quadratic function.? f(x)=x2−5xf ( x ) = x ^ { 2 } - 5 xf(x)=x2−5x ?

?Write the standard form of the equation of the parabola that has a vertex at (-6,-5)and passes through the point (-8,6). ?

Select the graph of the function y=x2+4y = x ^ { 2 } + 4y=x2+4 .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 and whose sum of the first number and four times the second is 160.

Select the graph of the function y=(x−4)2+1y = ( x - 4 ) ^ { 2 } + 1y=(x−4)2+1 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 . ?

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

Compare the graph of n=[−19(x+6)]2−1n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1n=[−91​(x+6)]2−1 with n(x)=x2n ( x ) = x ^ { 2 }n(x)=x2 .

Graph the quadratic function. ​ F (x)= x2 + 2x ​

Find the vertex of the parabolic graph of the equation. y = 4(x - 5)2 + 7

Graph the quadratic function. ​ F (x)= - 4x2 + 2 ​

The profit P (in hundreds of dollars)that a company makes depends on the amount x (in hundreds of dollars)the company spends on advertising according to the model? P=230+30x−0.5x2P = 230 + 30 x - 0.5 x ^ { 2 }P=230+30x−0.5x2 ? What expenditure for advertising will yield a maximum profit? ?

Write the quadratic function f(x)=x2+2x+5f ( x ) = x ^ { 2 } + 2 x + 5f(x)=x2+2x+5 in standard form.

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

Write the standard form of the equation of the parabola that has a vertex at $\left( - \frac { 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 2,3 )$ .

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

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

The total revenue R earned (in thousands of dollars)from manufacturing handheld video games is given by? $R ( p ) = - 25 p ^ { 2 } + 1200 p$ ? where p is the price per unit (in dollars). ? Find the revenue when the price per unit is $20. ?

Find the inverse of the one-to-one function.? $y = 7 x + 5$ ?

Select the graph of the quadratic function.? $f ( x ) = x ^ { 2 } - 5 x$ ?

Select the graph of the function $y = x ^ { 2 } + 4$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

Select the graph of the function $y = ( x - 4 ) ^ { 2 } + 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ . ?

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

Compare the graph of $n = \left[ - \frac { 1 } { 9 } ( x + 6 ) \right] ^ { 2 } - 1$ with $n ( x ) = x ^ { 2 }$ .

Graph the quadratic function. F (x)= x² + 2x

Find the vertex of the parabolic graph of the equation. y = 4(x - 5)² + 7

Graph the quadratic function. F (x)= - 4x² + 2

The profit P (in hundreds of dollars)that a company makes depends on the amount x (in hundreds of dollars)the company spends on advertising according to the model? $P = 230 + 30 x - 0.5 x ^ { 2 }$ ? What expenditure for advertising will yield a maximum profit? ?

Write the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 5$ in standard form.