Polynomial And Rational Functions Test Bank Docx Chapter 4 - Test Bank | College Algebra 5e by Young by Cynthia Y. Young. DOCX document preview.

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Polynomial And Rational Functions Test Bank Docx Chapter 4

College Algebra, 5e (Young)

Chapter 4 Polynomial and Rational Functions

4.1 Quadratic Functions

1) Rewrite the quadratic equation in standard form by completing the square.

y = (x) with superscript (2) - 8x + 19

A) y = ((x - 4)) with superscript (2) + 3

B) y = ((x + 4)) with superscript (2) + 3

C) y = ((x - 16)) with superscript (2) + 35

D) y = ((x + 16)) with superscript (2) + 35

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Find the equation of a parabola.

2) Rewrite the quadratic equation in standard form by completing the square.

y = (x) with superscript (2) + 4x - 20

A) y = ((x + 2)) with superscript (2) + 16

B) y = ((x - 2)) with superscript (2) - 24

C) y = ((x + 2)) with superscript (2) - 16

D) y = ((x + 2)) with superscript (2) - 24

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Find the equation of a parabola.

3) Rewrite the quadratic function in standard form by completing the square.

y = -(x) with superscript (2) - 14x + 3

A) y = (-(x + 7)) with superscript (2) - 46

B) y = (-(x - 7)) with superscript (2) + 21

C) y = (-(x + 7)) with superscript (2) + 52

D) y = ((x + 7)) with superscript (2) - 46

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Find the equation of a parabola.

4) Rewrite the quadratic equation in standard form by completing the square.

y = (x) with superscript (2) - 1x

A) y = ((x + 1/2)) with superscript (2) - 1/4

B) y = ((x - 1/2)) with superscript (2)

C) y = ((x - 1/2)) with superscript (2) - 1/4

D) y = ((x - 1)) with superscript (2) + 1/4

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Find the equation of a parabola.

5) Find the vertex of the parabola associated with the quadratic function.

y = ((x - 1)) with superscript (2) + 23

A) (-1, -23)

B) (1, -23)

C) (-1, 23)

D) (1, 23)

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function in standard form.

6) Find the vertex of the parabola associated with the quadratic function.

y = (-(x - 8)) with superscript (2) + 10

A) (8, -10)

B) (-8, -10)

C) (8, 10)

D) (-8, 10)

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function in standard form.

7) Find the vertex of the parabola associated with the quadratic equation.

y = ((x + 1/2)) with superscript (2) - 3

A) (-1/2, -3)

B) (1/2, -3)

C) (-1/2, 3)

D) (1/2, 3)

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function in standard form.

8) Find the vertex of the parabola associated with the quadratic function.

y = -5((x + 14)) with superscript (2) + 8

A) (14, -8)

B) (14, 8)

C) (-14, 8)

D) (-5, 8)

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function in standard form.

9) Find the vertex of the parabola associated with the quadratic function.

y = (x) with superscript (2) + 6x + 22

A) (3, -13)

B) (-3, -13)

C) (-3, 13)

D) (3, 13)

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function given in general form.

10) Find the vertex of the parabola associated with the quadratic function.

y = -(x) with superscript (2) + 4x + 6

A) (-2, 34)

B) (2, 10)

C) (2, 34)

D) (-2, 10)

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function given in general form.

11) Find the standard form of the equation of a parabola whose vertex is (2, 9) and passes through the point (7, -116).

A) y = -5((x - 2)) with superscript (2) + 9

B) y = - (107/81)((x + 2)) with superscript (2) - 9

C) y = - (125/811)((x + 2)) with superscript (2) + 9

D) y = - (107/25)((x - 2)) with superscript (2) - 9

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function in standard form.

12) Find the general form of the equation of a parabola whose vertex is (2, 1.5) and passes through the point (1, 0.3).

A) y = -1.2(x) with superscript (2) + 4.8x - 3.3

B) y = -1.2(x) with superscript (2) + 4.8x + 3.3

C) y = 1.2(x) with superscript (2) + 4.8x - 3.3

D) y = 1.2(x) with superscript (2) + 4.8x + 3.3

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function given in general form.

13) A rancher has 3000 linear feet of fencing and wants to enclose a rectangular field and then divide it into two equal pastures with an internal fence parallel to one of the rectangular sides. What is the maximum area of each pasture?

A) 187,500 square feet

B) 15,000 square feet

C) 375,000 square feet

D) 360,000 square feet

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Find the equation of a parabola.

14) Rewrite the quadratic function in standard form by completing the square.

y = 4(x) with superscript (2) - 48x + 130

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Find the equation of a parabola.

15) Find the vertex of the parabola associated with the quadratic function.

y = -4(x) with superscript (2) + 76x - 370.5

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function given in general form.

16) A rancher has 1,800 linear feet of fencing and wants to enclose a rectangular field and then divide it into two equal pastures with an internal fence parallel to one of the rectangular sides. What is the maximum area of each pasture?

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function given in general form.

17) Find the standard form of the equation of a parabola whose vertex is (5, 10) and passes through the point (3, 30).

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function in standard form.

18) Find the standard form of the equation of a parabola whose vertex is (8, 4.1) and passes through the point (-2.5, 158.45).

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function in standard form.

19) Graph the quadratic function given in standard form.

An equation reads, f of x equals negative left parenthesis x plus 4 right parenthesis squared plus 1.

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 9 to 1, in increments of 0.5. The y axis ranges from negative 18 to 2, in increments of 2. The parabola opens downward, with its vertex at (negative 4, 1). The parabola passes through the points (negative 8, negative 14.5) and (0, negative 14.5). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function in standard form.

20) Graph the quadratic function given in standard form.

An equation reads, f of x equals negative 3 left parenthesis x minus 2 right parenthesis squared plus 5.

A)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 1 to 5, in increments of 1. The y axis ranges from negative 10 to 6, in increments of 2. The parabola opens downward, with its vertex at (2, 5). The parabola passes through the points (0, negative 7) and (4, negative 7). All values are estimated.

B)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 5 to 1, in increments of 1. The y axis ranges from negative 10 to 6, in increments of 2. The parabola opens downward, with its vertex at (negative 2, 5). The parabola passes through the points (negative 4, negative 7) and (0, negative 7). All values are estimated.

C)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 1 to 5, in increments of 1. The y axis ranges from negative 7 to 9, in increments of 2. The parabola opens upward, with its vertex at (2, negative 5). The parabola passes through the points (0, 7) and (4, 7). All values are estimated.

D)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 5 to 1, in increments of 1. The y axis ranges from negative 7 to 9, in increments of 2. The parabola opens upward, with its vertex at (negative 2, negative 5). The parabola passes through the points (negative 4, 7) and (0, 7). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function in standard form.

21) Graph the quadratic function.

An equation reads, f of x equals 3 x squared minus 12 x plus 7.

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 1 to 5, in increments of 1. The y axis ranges from negative 7 to 9, in increments of 2. The parabola opens upward, with its vertex at (2, negative 5). The parabola passes through the points (0, 7), (0.5, 0), (3.2, 0), and (4.5, 10). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function given in general form.

22) Graph the quadratic function.

f of x equals one-half times x squared plus x minus one-half.

A)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 5 to 3, in increments of 0.5. The y axis ranges from negative 2 to 6, in increments of 0.5. The parabola opens upward, with its vertex at (negative 1, negative 1). The parabola passes through the points (negative 4, 4), (negative 2.5, 0), (0, negative 0.5), (0.5, 0) and (2.5, 4). All values are estimated.

B)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 3 to 5, in increments of 0.5. The y axis ranges from negative 5 to 2, in increments of 0.5. The parabola opens downward, with its vertex at (1, 1). The parabola passes through the points (negative 2.5, negative 5), (negative 0.5, 0), (0, 0.5), and (2.4, 0). All values are estimated.

C)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 5 to 3, in increments of 0.5. The y axis ranges from negative 5 to 2, in increments of 0.5. The parabola opens downward, with its vertex at (negative 1, 1). The parabola passes through the points (negative 4.5, negative 5), (negative 2.5, 0), (0, 0.5), and (0.4, 0). All values are estimated.

D)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 3 to 5, in increments of 0.5. The y axis ranges from negative 2 to 5, in increments of 0.5. The parabola opens upward, with its vertex at (1, negative 1). The parabola passes through the points (negative 2, 4), (negative 0.5, 0), (0, negative 0.6), and (2.5, 0). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function given in general form.

23) Match the quadratic function to an equation in standard form.

A parabola is graphed on an x y coordinate plane. The x axis ranges from 0 to 8, in increments of 2. The y axis ranges from negative 4 to 14, in increments of 2. The parabola opens upward, with its vertex at (4, negative 3). The parabola passes through the points (0, 13), (2.1, 0), (5.9, 0) and (8, 13). All values are estimated.

A) f of x equals left parenthesis x minus 4 right parenthesis squared minus 3.

B) f of x equals left parenthesis x plus 4 right parenthesis squared minus 3.

C) f of x equals negative left parenthesis x minus 4 right parenthesis squared plus 3.

D) f of x equals negative left parenthesis x plus 4 right parenthesis squared plus 3.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Find the equation of a parabola.

24) Rewrite the quadratic function in standard form by completing the square.

f of x equals negative 3 times x squared minus 6 times x minus 1.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Find the equation of a parabola.

25) A person standing near the edge of a cliff 150 feet above a lake throws a rock upward with an initial speed of 40 feet per second. The height of the rock above the lake at the bottom of the cliff is a function of time and is described by

h(t) = -16(t) with superscript (2) + 40t + 150

a. How many seconds will it take until the rock reaches its maximum height?

What is that height?

b. At what time will the rock hit the water? Round to two decimal places.

175 feet

Part B: 4.56 seconds

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Find the equation of a parabola.

26) The concentration of a drug in the bloodstream, measured in parts per million, can be modeled with a quadratic function. In 67 minutes the concentration is 49.266 parts per million. The maximum concentration of the drug in the bloodstream occurs in 300 minutes and is 375 parts per million.

a. Find a quadratic function that models the concentration of the drug as a function of time in minutes.

b. In how many minutes will the drug be eliminated from the bloodstream?

Part B: 550 minutes

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Find the equation of a parabola.

27) Graph the quadratic function.

y = ((x) with superscript (2) - 1) - 1

A blank Cartesian grid. Both the axes range from negative 5 to 5, in increments of 1.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function in standard form.

28) Graph the quadratic function.

y = (x) with superscript (2) + 2x + 4

A blank Cartesian grid. Both the axes range from negative 5 to 5, in increments of 1.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 01

Learning Objective: Graph a quadratic function given in general form.

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Document Type:
DOCX
Chapter Number:
4
Created Date:
Aug 21, 2025
Chapter Name:
Chapter 4 Polynomial And Rational Functions
Author:
Cynthia Y. Young

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