Exam 3: Polynomial and Rational Functions

Solve the problem. -The owner of a video store has determined that the profits $\mathrm { P }$ of the store are approximately given by $P ( x ) = - x ^ { 2 } + 120 x + 67$ , where $x$ is the number of videos rented daily. Find the maximum profit to the nearest dollar.

(Multiple Choice)

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Question 21

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 8 - ( x + 5 ) ^ { 2 }$

(Multiple Choice)

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Question 22

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $y + 4 = ( x - 2 ) ^ { 2 }$

(Multiple Choice)

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Question 23

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = 4 x ^ { 2 } - 5 x - 9$

(Multiple Choice)

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Question 24

Determine a Quadratic Function's Minimum or Maximum Value Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = 3 x ^ { 2 } + 2 x - 2$

(Multiple Choice)

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Question 25

Find the range of the quadratic function. - $f ( x ) = 11 ( x - 2 ) ^ { 2 } + 8$

(Multiple Choice)

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Question 26

Find the x-intercepts (if any)for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 4$

(Multiple Choice)

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Question 27

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 5 x ^ { 2 }$ , but which has a minimum of 9 at $x = 5$ .

(Multiple Choice)

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Question 28

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = - x ^ { 2 } + 14 x - 6$

(Multiple Choice)

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Question 29

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 11 x ^ { 2 }$ , but which has its vertex at $( 3,7 )$ .

(Multiple Choice)

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Question 30

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 4 x ^ { 2 } - 8 x + 7$

(Multiple Choice)

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Question 31

Find the domain and range of the quadratic function whose graph is described. -The minimum is 15 at $x = - 1$ .

(Multiple Choice)

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Question 32

Find the x-intercepts (if any)for the graph of the quadratic function. - $3 x ^ { 2 } + 10 x + 6 = 0$ Give your answers in exact form.

(Multiple Choice)

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Question 33

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x - 5 ) ^ { 2 } - 5$

(Multiple Choice)

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Question 34

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f(x)=-4(x+5)^{2}+1$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=-4(x+5)^{2}+1$

(Multiple Choice)

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Question 35

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f(x)=-3 x^{2}-30 x-74$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=-3 x^{2}-30 x-74$

(Multiple Choice)

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Question 36

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 8 - x ^ { 2 } + 2 x$

(Multiple Choice)

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Question 37

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 9$

(Multiple Choice)

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Question 38

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = 4 - ( x + 3 ) ^ { 2 }$

(Multiple Choice)

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Question 39

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 5$

(Multiple Choice)

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Question 40

Solve the problem. -The owner of a video store has determined that the profits $\mathrm { P }$ of the store are approximately given by $P ( x ) = - x ^ { 2 } + 120 x + 67$ , where $x$ is the number of videos rented daily. Find the maximum profit to the nearest dollar.

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 8 - ( x + 5 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $y + 4 = ( x - 2 ) ^ { 2 }$

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = 4 x ^ { 2 } - 5 x - 9$

Determine a Quadratic Function's Minimum or Maximum Value Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = 3 x ^ { 2 } + 2 x - 2$

Find the range of the quadratic function. - $f ( x ) = 11 ( x - 2 ) ^ { 2 } + 8$

Find the x-intercepts (if any)for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 4$

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 5 x ^ { 2 }$ , but which has a minimum of 9 at $x = 5$ .

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = - x ^ { 2 } + 14 x - 6$

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 11 x ^ { 2 }$ , but which has its vertex at $( 3,7 )$ .

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 4 x ^ { 2 } - 8 x + 7$

Find the domain and range of the quadratic function whose graph is described. -The minimum is 15 at $x = - 1$ .

Find the x-intercepts (if any)for the graph of the quadratic function. - $3 x ^ { 2 } + 10 x + 6 = 0$ Give your answers in exact form.

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x - 5 ) ^ { 2 } - 5$

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f(x)=-4(x+5)^{2}+1$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=-4(x+5)^{2}+1$

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f(x)=-3 x^{2}-30 x-74$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=-3 x^{2}-30 x-74$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 8 - x ^ { 2 } + 2 x$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 9$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = 4 - ( x + 3 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 5$

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences, Induction, and Probability

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Exam 3: Polynomial and Rational Functions

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=8−(x+5)2f ( x ) = 8 - ( x + 5 ) ^ { 2 }f(x)=8−(x+5)2

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - y+4=(x−2)2y + 4 = ( x - 2 ) ^ { 2 }y+4=(x−2)2

Find the y-intercept for the graph of the quadratic function. - f(x)=4x2−5x−9f ( x ) = 4 x ^ { 2 } - 5 x - 9f(x)=4x2−5x−9

Determine a Quadratic Function's Minimum or Maximum Value Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - f(x)=3x2+2x−2f ( x ) = 3 x ^ { 2 } + 2 x - 2f(x)=3x2+2x−2

Find the range of the quadratic function. - f(x)=11(x−2)2+8f ( x ) = 11 ( x - 2 ) ^ { 2 } + 8f(x)=11(x−2)2+8

Find the x-intercepts (if any)for the graph of the quadratic function. - f(x)=x2−4f ( x ) = x ^ { 2 } - 4f(x)=x2−4

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of f(x)=5x2f ( x ) = 5 x ^ { 2 }f(x)=5x2 , but which has a minimum of 9 at x=5x = 5x=5 .

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=−x2+14x−6f ( x ) = - x ^ { 2 } + 14 x - 6f(x)=−x2+14x−6

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of f(x)=11x2f ( x ) = 11 x ^ { 2 }f(x)=11x2 , but which has its vertex at (3,7)( 3,7 )(3,7) .

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=4x2−8x+7f ( x ) = 4 x ^ { 2 } - 8 x + 7f(x)=4x2−8x+7

Find the domain and range of the quadratic function whose graph is described. -The minimum is 15 at x=−1x = - 1x=−1 .

Find the x-intercepts (if any)for the graph of the quadratic function. - 3x2+10x+6=03 x ^ { 2 } + 10 x + 6 = 03x2+10x+6=0 Give your answers in exact form.

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=(x−5)2−5f ( x ) = ( x - 5 ) ^ { 2 } - 5f(x)=(x−5)2−5

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=−4(x+5)2+1f(x)=-4(x+5)^{2}+1f(x)=−4(x+5)2+1

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=−3x2−30x−74f(x)=-3 x^{2}-30 x-74f(x)=−3x2−30x−74

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=8−x2+2xf ( x ) = 8 - x ^ { 2 } + 2 xf(x)=8−x2+2x

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=−7(x−3)2−9f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 9f(x)=−7(x−3)2−9

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=4−(x+3)2f ( x ) = 4 - ( x + 3 ) ^ { 2 }f(x)=4−(x+3)2

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences, Induction, and Probability

Filters

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 8 - ( x + 5 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $y + 4 = ( x - 2 ) ^ { 2 }$

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = 4 x ^ { 2 } - 5 x - 9$

Determine a Quadratic Function's Minimum or Maximum Value Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = 3 x ^ { 2 } + 2 x - 2$

Find the range of the quadratic function. - $f ( x ) = 11 ( x - 2 ) ^ { 2 } + 8$

Find the x-intercepts (if any)for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 4$

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 5 x ^ { 2 }$ , but which has a minimum of 9 at $x = 5$ .

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = - x ^ { 2 } + 14 x - 6$

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 11 x ^ { 2 }$ , but which has its vertex at $( 3,7 )$ .

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 4 x ^ { 2 } - 8 x + 7$

Find the domain and range of the quadratic function whose graph is described. -The minimum is 15 at $x = - 1$ .

Find the x-intercepts (if any)for the graph of the quadratic function. - $3 x ^ { 2 } + 10 x + 6 = 0$ Give your answers in exact form.

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x - 5 ) ^ { 2 } - 5$

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f(x)=-4(x+5)^{2}+1$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=-4(x+5)^{2}+1$

Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - $f(x)=-3 x^{2}-30 x-74$ $Graph Parabolas Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=-3 x^{2}-30 x-74$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 8 - x ^ { 2 } + 2 x$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 9$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = 4 - ( x + 3 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 5$