Ch8 Test Bank Conics And Systems Of Nonlinear Equations And - Test Bank | College Algebra 5e by Young by Cynthia Y. Young. DOCX document preview.

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Ch8 Test Bank Conics And Systems Of Nonlinear Equations And

College Algebra, 5e (Young)

Chapter 8 Conics and Systems of Nonlinear Equations and Inequalities

8.2 The Parabola

1) Find an equation for the parabola with vertex (4, 5) and focus (4, 11).

A) ((x - 4)) with superscript (2) = 24( y - 5)

B) ((x - 5)) with superscript (2) = 24( y - 4)

C) ((x - 4)) with superscript (2) = 6( y - 5)

D) ((x + 4)) with superscript (2) = 24( y + 5)

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

2) Find an equation for the parabola with vertex (1, 8) and focus (3, 8).

A) (( y - 8)) with superscript (2) = -2(x - 1)

B) (( y + 8)) with superscript (2) = -8(x + 1)

C) (( y - 8)) with superscript (2) = -8(x - 1)

D) ((x - 8)) with superscript (2) = -8( y - 1)

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

3) Find an equation for the parabola with vertex (2, 8) and focus (4, 8).

A) (x) with superscript (2) - 16x - 8y + 48 = 0

B) ( y) with superscript (2) - 16y - 8x + 48 = 0

C) ( y) with superscript (2) - 16y + 8x + 48 = 0

D) (x) with superscript (2) - 16x + 8y + 48 = 0

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

4) Find an equation for the parabola with vertex (-2, 10) and focus (-5, 10).

A) ( y) with superscript (2) - 20y + 12x + 124 = 0

B) (x) with superscript (2) - 20x + 12y + 124 = 0

C) (x) with superscript (2) - 20x - 12y + 124 = 0

D) ( y) with superscript (2) - 20y - 12x + 124 = 0

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

5) Find an equation for the parabola with vertex (8, 3) and focus (8, 10).

A) ( y) with superscript (2) - 16y - 28x + 148 = 0

B) (x) with superscript (2) - 16x + 28y + 148 = 0

C) (x) with superscript (2) - 16x - 28y + 148 = 0

D) ( y) with superscript (2) - 16y + 28x + 148 = 0

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

6) Find an equation for the parabola with vertex (7, 1) and focus (7, -5).

A) (x) with superscript (2) - 14x + 24y + 25 = 0

B) (x) with superscript (2) - 14x - 24y + 25 = 0

C) ( y) with superscript (2) - 14y - 24x + 25 = 0

D) ( y) with superscript (2) + 14y + 24x + 25 = 0

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

7) Find an equation for the parabola with focus (14, 3) and directrix x = 4.

A) (x) with superscript (2) - 6x + 20y + 189 = 0

B) (x) with superscript (2) - 6x - 20y + 189 = 0

C) ( y) with superscript (2) - 6y - 20x + 189 = 0

D) ( y) with superscript (2) - 6y + 20x + 189 = 0

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

8) Find an equation for the parabola with focus (9, 7) and directrix x = 11.

A) ( y) with superscript (2) - 14y - 4x + 9 = 0

B) ( y) with superscript (2) - 14y + 4x + 9 = 0

C) (x) with superscript (2) - 14x - 4y + 9 = 0

D) (x) with superscript (2) - 14x + 4y + 9 = 0

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

9) Find an equation for the parabola with focus (1, 11) and directrix y = 7.

A) ( y) with superscript (2) - 2y - 8x + 73 = 0

B) (x) with superscript (2) - 2x - 8y + 73 = 0

C) (x) with superscript (2) - 2x + 8y + 73 = 0

D) ( y) with superscript (2) - 2y + 8x + 73 = 0

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

10) Find an equation for the parabola with focus (8, -2) and directrix y = 4.

A) (x) with superscript (2) - 16x + 12y + 52 = 0

B) (x) with superscript (2) - 16x - 12y + 52 = 0

C) ( y) with superscript (2) - 16x + 12y + 52 = 0

D) ( y) with superscript (2) - 16x - 12y + 52 = 0

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

11) Find an equation of the form A(x) with superscript (2) + Bx + Cy + D = 0 or A(y) with superscript (2) + By + Cx + D = 0 for the parabola with vertex (-1, 6) and focus (5, 6).

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

12) Find an equation of the form A(x) with superscript (2) + Bx + Cy + D = 0 or A(y) with superscript (2) + By + Cx + D = 0 for the parabola with focus (10, -8) and directrix y = 8.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

13) Graph the equation.

x squared equals negative one-fourth times y.

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 3 to 3, in increments of 0.5. The y axis ranges from negative 8 to 2, in increments of 0.5. The parabola opens downward, with its vertex at (0, 0). The parabola passes through the points (negative 1, negative 3) and (1, negative 3). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

14) Write an equation for the parabola.

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

x squared equals one-fifth times y.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

15) Match the parabola to the equation.

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

A) x squared equals negative one-fifth times y.

B) y squared equals one-fourth times x.

C) y squared equals negative one-fourth times x.

D) x squared equals one-fifth times y.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

16) Match the equation to the parabola.

An equation reads, x squared equals negative (1 over 5) times y.

A)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 2 in increments of 1. The vertical axis ranges from negative 8 to 1 in increments of 1. The parabola opens downward, with its vertex at (0, 0). The parabola passes through (negative 1, negative 5) and (1, negative 5). All values are estimated.

B)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 8, in increments of 1. The y axis ranges from negative 2 to 1, in increments of 1. The parabola opens rightward, with its vertex at (0, 0). The parabola passes through the points (5, negative 1) and (5, 1). All values are estimated.

C)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 2, in increments of 1. The y axis ranges from negative 2 to 1, in increments of 1. The parabola opens leftward, with its vertex at (0, 0). The parabola passes through the points (negative 5, 1) and (negative 5, negative 1). All values are estimated.

D)

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

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

17) Graph the parabola and label the coordinates of the vertex.

An equation reads, left parenthesis x plus 2 right parenthesis squared equals negative 2 times left parenthesis y plus 3 right parenthesis.

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 4 in increments of 1. The y axis ranges from negative 10 to 6 in increments of 1. The parabola opens downward, with its vertex at (negative 2, negative 3).The parabola passes through the points (negative 7, negative 8), (0, negative 5), and (2, negative 10). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

18) Graph the parabola and label the coordinates of the vertex.

An equation reads, y squared minus 4 x plus 2 y minus 3 equals 0.

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 10, in increments of 1. The y axis ranges from negative 8 to 6, in increments of 1. The parabola opens rightward, with its vertex at (negative 1, negative 1). The parabola passes through the points (6, 4), (0, 1), (negative 0.9, 0), (0, negative 3), and (4, negative 6). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

19) Match the parabola to an equation in standard form.

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 6 in increments of 1. The y axis ranges from negative 10 to 4 in increments of 1. The parabola opens downward, with its vertex at (negative 1, 1). The parabola passes through the points (negative 6, negative 6), (negative 3, 0), (0, 1), (1, 0), and (4, negative 6). All values are estimated.

A) An equation reads, left parenthesis x plus 1 right parenthesis squared equals negative 4 times left parenthesis y minus 1 right parenthesis.

B) An equation reads, left parenthesis x minus 1 right parenthesis squared equals 4 times left parenthesis y plus 1 right parenthesis.

C) An equation reads, left parenthesis x minus 1 right parenthesis squared equals negative 4 times left parenthesis y plus 1 right parenthesis.

D) An equation reads, left parenthesis x plus 1 right parenthesis squared equals 4 times left parenthesis y minus 1 right parenthesis.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

20) Match the parabola to an equation in general form.

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 10 in increments of 1. The y axis ranges from negative 10 to 2 in increments of 1. The parabola opens downward, with its vertex at (3, negative 1). The parabola passes through the points (negative 2, negative 10), (0, negative 4), and (6, negative 4). All values are estimated.

A) An equation reads, x squared minus 6 x plus 3 y plus 12 equals 0.

B) An equation reads, x squared plus 6 x minus 3 y plus 6 equals 0.

C) An equation reads, x squared minus 6 x plus 3 y plus 6 equals 0.

D) An equation reads, x squared plus 6 x minus 3 y plus 12 equals 0.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

21) Match the equation to the parabola.

An equation reads, left parenthesis y minus 1 right parenthesis squared equals 4 times left parenthesis x minus 1 right parenthesis.

A)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 10, in increments of 1. The y axis ranges from negative 6 to 8, in increments of 1. The parabola opens rightward, with its vertex at (1, 1). The parabola passes through the points (4, 4), (0, 1.2), and (4, negative 2.5). All values are estimated.

B)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 4, in increments of 1. The y axis ranges from negative 6 to 8, in increments of 1. The parabola opens leftward, with its vertex at (1, 1). The parabola passes through the points (negative 6, 6), (0, 3), (0.9, 0), (0, negative 1), and (negative 6, negative 4). All values are estimated.

C)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 10, in increments of 1. The y axis ranges from negative 8 to 6, in increments of 1. The parabola opens rightward, with its vertex at (negative 1, negative 1). The parabola passes through the points (6, 4), (0, 1), (negative 0.8, 0), (0, negative 3), and (5, negative 6). All values are estimated.

D)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 4, in increments of 1. The y axis ranges from negative 8 to 6, in increments of 1. The parabola opens leftward, with its vertex at (negative 1, negative 1). The parabola passes through the points (negative 8, 4.5), (negative 1.2, 0), and (negative 7.5, negative 6). All values are estimated.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

22) Match the equation to the parabola.

An equation reads, x squared minus 6 x plus 3 y plus 6 equals 0.

A)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 10 in increments of 1. The y axis ranges from negative 8 to 4 in increments of 1. The parabola opens downward, with its vertex at (3, 1). The parabola passes through the points (negative 2, negative 8), (0, negative 2), (0.9, 0), (4.9, 0), and (5.5, negative 6). All values are estimated.

B)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 4 in increments of 1. The y axis ranges from negative 2 to 10 in increments of 1. The parabola opens upward, with its vertex at (negative 3, 1). The parabola passes through the points (negative 8, 10), (0, 4), and (2, 9). All values are estimated.

C)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 10 in increments of 1. The y axis ranges from negative 10 to 2 in increments of 1. The parabola opens downward, with its vertex at (3, negative 1). The parabola passes through the points (negative 1, negative 6.5), (0, negative 4), and (7, negative 7). All values are estimated.

D)

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 4 in increments of 1. The y axis ranges from negative 4 to 8 in increments of 1. The parabola opens upward, with its vertex at (negative 3, negative 1). The parabola passes through the points (negative 7, 5), (negative 4.9, 0), (negative 1.1, 0), (0, 2), and (2, 7.5). All values are estimated.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

23) Write an equation for the parabola in standard form.

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 2, in increments of 1. The y axis ranges from negative 6 to 4, in increments of 1. The parabola opens leftward, with its vertex at (negative 3, negative 2). The parabola passes through the points (negative 9, 1.5), (negative 5, 0), and (negative 9, negative 5.5). All values are estimated.

An equation reads, left parenthesis y plus 2 right parenthesis squared equals negative 2 times left parenthesis x plus 3 right parenthesis.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

24) Write an equation for the parabola in standard form.

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 12 to 2, in increments of 1. The y axis ranges from negative 4 to 10, in increments of 1. The parabola opens leftward, with its vertex at (negative 1, 3). The parabola passes through the points (negative 4, 6), (negative 4, 0), and (negative 10, negative 2). All values are estimated.

An equation reads, left parenthesis y plus 3 right parenthesis squared equals 3 times left parenthesis x plus 1 right parenthesis.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

25) Write an equation for the parabola in general form.

A parabola is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 10 in increments of 1. The y axis ranges from negative 8 to 4 in increments of 1. The parabola opens downward, with its vertex at (3, 1). The parabola passes through the points (negative 1, negative 4), (0, negative 2), (1.2, 0), (4.9, 0), and (6, negative 2). All values are estimated.

An equation reads, x squared minus 6 x plus 3 y plus 6 equals 0.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

26) A satellite dish measures 72 feet across its opening and 9 feet deep at its center. The receiver should be placed at the focus of the parabolic dish. Where is the focus?

A) The focus will be at (0, 9) so the receiver should be placed 36 feet from the vertex.

B) The focus will be at (0, 36) so the receiver should be placed 9 feet from the vertex.

C) The focus will be at (36, 0) so the receiver should be placed 9 feet from the vertex.

D) The focus will be at (0, 36) so the receiver should be placed 72 feet from the vertex.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the origin.

27) A bridge with a parabolic shape has an opening 98 feet wide at the base of the bridge (where the bridge meets the water), and the height in the center of the bridge is 40 feet. A sailboat whose mast reaches 50 feet above the water is traveling under the bridge 23 feet from the center of the bridge. Will it clear the bridge without scraping its mast? Justify your answer.

A) No. The opening height is 50 feet, and the mast is 31.2 feet.

B) Yes. The opening height is 50 feet, and the mast is 31.2 feet.

C) No. The opening height is 31.2 feet, and the mast is 50 feet.

D) No. The opening height is 32 feet, and the mast is 50 feet.

Diff: 3 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the origin.

28) Find the vertex of the parabola with equation ((x - 8)) with superscript (2) = 20( y - 9).

Diff: 1 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

29) Find the vertex of the parabola with equation (( y - 1)) with superscript (2) = -24(x - 4).

Diff: 1 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

30) Find the vertex of the parabola with equation (y) with superscript (2) - 14y - 24x + 25 = 0.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

31) Find the vertex of the parabola with equation (y) with superscript (2) - 2y + 8x + 41 = 0.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

32) Find the focus of the parabola with equation ((x - 3)) with superscript (2) = 24( y - 8).

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

33) Find the focus of the parabola with equation (( y - 4)) with superscript (2) = -12(x - 2).

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

34) Find the focus of the parabola with equation (y) with superscript (2) - 16y - 4x + 4 = 0.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

35) Find the focus of the parabola with equation (y) with superscript (2) - 14y + 32x + 209 = 0.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

36) Find the equation of the directrix of the parabola with equation ((x - 4)) with superscript (2) = 12( y - 5).

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

37) Find the equation of the directrix of the parabola with equation (( y - 6)) with superscript (2) = -8(x - 3).

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

38) Find the equation of the directrix of the parabola with equation ( y) with superscript (2) - 12y - 12x + 12 = 0.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

39) Find the equation of the directrix of the parabola with equation (x) with superscript (2) - 6x - 32y + 201 = 0.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

40) Find the length of the latus rectum of the parabola with equation ((x - 1)) with superscript (2) = 20( y - 4).

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

41) Find the length of the latus rectum of the parabola with equation (( y - 5)) with superscript (2) = -8(x - 7).

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

42) Find the length of the latus rectum of the parabola with equation ( y) with superscript (2) - 18y - 4x + 77 = 0.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

43) Find the length of the latus rectum of the parabola with equation (x) with superscript (2) - 16x - 8y + 120 = 0.

Diff: 2 Var: 1

Chapter/Section: Ch 08, Sec 02

Learning Objective: Graph a parabola given the focus, directrix, and vertex.

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Document Information

Document Type:
DOCX
Chapter Number:
8
Created Date:
Aug 21, 2025
Chapter Name:
Chapter 8 Conics And Systems Of Nonlinear Equations And Inequalities
Author:
Cynthia Y. Young

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