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SCORE C

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PDF 2nd

Chapter 9 67 Glencoe Algebra 2

9

1. Find the midpoint of the line segment with endpoints at (-12, 3.5) and (5.1, 4.8).

2. Find the distance between A(4 ! " 5 , -2) and B( ! " 5 , 9).

3. Write the equation x = -y2 + 6y - 7 in standard form.

4. Write an equation for the parabola with vertex (-5, 1) and

directrix x = - 7 # 2 .

5. MODEL PLANES The path traveled by Pati’s remote-controlledmodel airplane is shaped like a parabola. It took off from the ground and landed on the ground 160 feet away from where it took off. If the airplane reached a maximum height of 40 feet, write an equation for the parabola that models the path of the plane. Assume that the point of take-off is the origin.

6. Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with equation x = -y2 - 2y + 9.

7. Write an equation for a circle if its center is in the first quadrant, and it is tangent to x = -2, x = 8 and the x-axis.

8. Graph x2 + y2 - 4x + 2y - 3 = 0.

9. Graph 5x2 - 2y2 - 4y = 22.

For Questions 10 and 11, write an equation for the ellipse that satisfies each set of conditions.

10. major axis 14 units long and parallel to the x-axis, minor

axis 10 units long, center at (5, - 1 # 2 )

11. endpoints of major axis at (3, -8) and (3, 4), foci at (3, -2 + 2 ! " 5 ) and (3, -2 - 2 ! " 5 )

Chapter 9 Test, Form 3

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

(10, -1); ( 39 ! 4 , -1)

y = -1; = 41 ! 4 ; left

y = - 1 ! 160

(x - 80)2 + 40

x = - 1 ! 6 (y - 1)2 - 5

x = -(y - 3)2 + 2

" ## 166 units

(-3.45, 4.15)

(y + 2)2

! 36

+ (x - 3)2

! 16

= 1

(x - 5)2

! 49

+ (y + 1 !

2 )

2

!

25 = 1

(x - 3)2 + (y - 5)2 = 25

y

xO 2

2

4-2-4

-2

y

xO 2

2

4-2-4

-2

-4

063_074_ALG2_A_CRM_C09_AS_660546.indd 67 12/12/12 8:54 AM

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

NAME DATE PERIOD

PDF 2nd

Chapter 9 68 Glencoe Algebra 2

9

12. Find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse with equation 6x2 + 5y2 - 24x - 30y = -39.

13. Write an equation for the hyperbola with vertices (4, -5) and (4, 1) and foci (4, 3) and (4, -7).

For Questions 14 and 15 write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.

14. 2x2 + 3y2 - 15 = 4(x - 2y)

15. 1 ! 8 x + y2 = -(y + 12)

For Questions 16 and 17, state whether the graph of each equation is a parabola, circle, ellipse, or hyperbola. State the values used to identify each conic section without writing each equation in standard form.

16. 3x2 - 9x + y2 = 2(24y - y2 - 27)

17. 34x2 + 40y2 - 18x - 25y = 17(2x2 + 1)

18. Find the exact solution(s) of the system of equations.

x2 !

25 -

y2

! 16

= 1

x = y

19. Solve the system of equations by graphing. x2 + y2 - 4x - 6y + 4 = 0 x2 - 4x - 3y + 4 = 0

20. Solve the system of inequalities by graphing. x2 + y2 - 4x > 62 - y < (x - 1.75)2

Bonus The parabolic curve of a certain camera lens can be represented by the equation y = 10x2 + 50x + 63.2. What are the coordinates of the vertex?

Chapter 9 Test, Form 3 (continued)

12.

13.

14.

15.

16.

17.

18.

19.

20.

(-1, 3), (5, 3), (2, 0)

no solution

parabola; A = 0, C = 40

circle; A = C

(2, 3); (2, 2), (2, 4); 2 ! " 6 ; 2 ! " 5

(y + 2)2

# 9 - (x - 4)2

# 16

= 1

(x - 1)2

# 67

# 6 +

(y + 4 # 3 )

2

#

67 # 9 = 1;

ellipse

x = -8 (y + 1 # 2 )

2

- 94;

parabola

(-2.5, 0.7)B:

y

xO 2

2

4 6-2

-2

y

xO

(5, 3)(–1, 3)

(2, 0)

2

2

4

6

4 6

063_074_ALG2_A_CRM_C09_AS_660546.indd 68 12/12/12 8:54 AM