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Graph the parabola.

Question : Graph the parabola. : 2163593

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Graph the parabola.

1) y = (x + 5)2

A)

B)

C)

D)

2) y = -4(x – 3)2 - 4

A)

B)

C)

D)

3) y = 4/5( x + 2)2 - 5

A)

B)

C)

D)

4) x = y2 - 2

A)

B)

C)

D)

5) x = (1/3)y2

A)

B)

C)

D)

6) x = 1/2(y + 1)2 + 3

A)

B)

C)

D)

7) y = x2 + 2x - 4

A)

B)

C)

D)

8) y = -x2 + 2x - 5

A)

B)

C)

D)

9) y = 2x2 - 2x - 9

A)

B)

C)

D)

10) y = -3x2 + 2x - 2

A)

B)

C)

D)

Find the vertex and axis of symmetry of the parabola.

11) x = y2 + 3

A) (0, 3); y = 3

B) (3, 0); x = 3

C) (3, 0); y = 0

D) (3, 0); x = 0

12) x = 1/2y2

A) (0, 0); x = 0

B) (2, 0); x = 2

C) (0, 0); y = 0

D) (2, 0); y = 0

13) x = 1/3(y + 2)2 - 2

A) (2, -2); y = -2

B) (2, 2); y = 2

C) (-2, -2); y = -2

D) (-2, -2); x = -2

14) y = 1/3(x – 1)2 + 2

A) (1, 2); y = 2

B) (-1, 2); y = 2

C) (2, 1); x = -1

D) (1, 2); x = 1

Use the graph to determine the equation of the parabola.

15)

A) y = x2 + 3

B) y = x2 - 3

C) x = y2 + 3

D) x = y2 - 3

16)

A) y = (x + 2)2 + 3

B) x = (y – 2)2 + 3 

C) x = (y + 2)2 + 3

D) y = (x - 2)2 - 3

Find the standard equation of the circle with the given radius r and center C.

17) r = 5 C = (-1, -4)

A) (x + 1)2 + (y + 4)2 = 25

B) (x – 4)2 + (y – 1)2 = 5

C) (x + 4)2 + (y + 1)2 = 5

D) (x – 1)2 + (y – 4)2 = 25

18) r = 2 C = (-1, 0)

A) (x – 1)2 + y2 = 4

B) x2 + (y + 1)2 = 2

C) (x + 1)2 + y2 = 4

D) x2 + (y – 1)2 = 2

19) r = Ö19 C = (-9, -8)

A) (x – 9)2 + (y – 8)2 = 19

B) (x + 8)2 + (y + 9)2 = 361

C) (x + 9)2 + (y + 8)2 = 19

D) (x – 8)2 + (y – 9)2 = 361

Use the graph to find the equation of the circle.

20)

A) x2 + y2 = 12

B) x2 + y2 = 36

C) x2 + y2 = 6

D) x2 + y2 = 16

21)

A) (x – 3)2 + (y – 2)2 = 4 

B) x2 + y2 = 16

C) (x + 3)2 + (y + 2)2 = 16

D) (x – 3)2 + (y - 2)2 = 16

Find the center and radius of the circle.

22) x2 + y2 = 25

A) (1, 1); 5

B) (0, 0); 25

C) (1, 1); 25

D) (0, 0); 5

23) (x – 4)2 + (y – 6)2 = 25

A) (6, 4); 5

B) (4, 6); 5

C) (6, 4); 25

D) (4, 6); 25

24) (x + 5)2 + (y – 9)2 = 36

A) (5, -9); 36

B) (-5, 9); 6

C) (-5, 9); 36

D) (5, -9); 6

25) x2 + y­2 + 2y = 8

A) (0, 2); 2

B) (1, 0); 4

C) (0, -1); 3

D) (0, 1); 3

26) x2 + 8x + y2 = 10y

A) (4, -5); Ö41

B) (-4, 5); Ö41

C) (4, 4); 3

D) (4, 5); 6

27) x2 + 4x + y2 = 5

A) (2, 0); 3

B) (0, -2); 2

C) (0, 2); 2

D) (-2, 0); 3

Solve the problem.

28) A radio telescope has the shape of a parabolic dish, whose cross section can be modeled by x = (35/8836)y2 where -94 ≤ y ≤ 94 and the units are feet. Find the depth d of the dish. 

A) 3290 ft

B) 8836 ft

C) 1225 ft

D) 35 ft

29) A parabolic train track must pass through the points (1, 0), (0, 8), and (0, -8), where the units are kilometers. Find an equation for the train tracks in the form x = a(y – h)2 + k.

A) x = 1/64(y – 0)2 - 1

B) x = - 1/64(y – 0)2 + 1

C) x = 1/64(y – 0)2 + 1

D) x = 1/8(y – 0)2 - 1

30) A comet travels in a parabolic path, given by x = -2.6y2, where the sun is located at (-0.1, 0) and the units are astronomical units (A.U.). Find the distance from the sun to the comet when the comet is located at (-10.4, -2). Round to the nearest hundredth when necessary.

A) 10.59 A.U.

B) 10.69 A.U.

C) 10.49 A.U.

D) 8.3 A.U.

Solution
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