10 Mid-Chapter Quiz

Do you know HOW?

Describe the graph and identify the domain and range for each equation.

1. y 2 − 2 x 2 = 16 y squared , minus , 2 x squared , equals 16
2. 3 x 2 + 3 y 2 − 12 = 0 3 x squared , plus 3 , y squared , minus 12 equals 0
3. 9 x 2 − 25 y 2 = 225 9 x squared , minus , 25 y squared , equals 225
4. 36 − 4 x 2 − 9 y 2 = 0 36 minus , 4 x squared , minus , 9 y squared , equals 0

Identify the vertex, focus, and directrix of each parabola. Then graph the parabola.

5. y = 3 x 2 y equals , 3 x squared
6. x = 4 ( y + 2 ) 2 x equals 4 . open y plus 2 close squared
7. y + 1 = ( x − 3 ) 2 y plus 1 equals . open x minus 3 close squared

Write an equation for the parabola with the given vertex and focus.

8. vertex ( − 5 , 4 ) ; negative 5 comma 4 close semicolon  focus ( − 5 , 0 ) negative 5 comma 0 close
9. vertex (7, 2); focus ( 7 , − 2 ) open 7 comma negative 2 close
10. vertex (0, 0); focus ( − 7 , 0 ) negative 7 comma 0 close
11. vertex (2, 4); focus (1, 4)

12. Write an equation that models the graph below.

    

Write an equation in standard form of the circle with the given center and radius.

13. center ( − 6 , 3 ) , negative 6 comma 3 close comma  radius 8
14. center (1, 1), radius 1.5

Do you UNDERSTAND?

Determine whether each point lies on the graph of the conic section with the given equation.

15. x 2 + y 2 = 36 x squared , plus . y squared , equals 36
    1. ( − 6 , 0 ) negative 6 comma 0 close
    2. ( − 2 , − 3 ) open . negative 2 comma negative square root of 3 . close
    3. ( 0 , 2 ) open , 0 comma square root of 2 , close
16. 4 x 2 − y 2 − 4 = 0 4 x squared , minus , y squared , minus 4 equals 0
    1. ( − 1 , 0 ) negative 1 comma 0 close
    2. (2, 2)
    3. (1, 0)

17. The table below represents points on the graph of a conic section. Identify the conic section.

    X	− 12 negative 12	− 8 negative 8	0	12
    Y	0	± 12 plus minus 12	± 16 plus minus 16	0

18. Writing Suppose that x 2 = 4 p y x squared , equals 4 p y  and y = a x 2 y equals , eh x squared  represent the same parabola. Explain how a and p are related.

Reasoning Without graphing, describe how each graph differs from the graph of y = x 2 . y equals , x squared , .

19. y = 2 x 2 y equals , 2 x squared
20. y =   − x 2 y equals , negative , x squared
21. y = x 2 + 2 y equals , x squared , plus 2
22. y = 1 3 x 2 y equals , 1 third , x squared
23. A circle has center (0, 0) and radius 1. Write an equation that represents the translation of the circle 7 units left and 8 units up. Then graph the equation.

Write the standard form of the equation of the circle that passes through the given point and whose center is at the origin.

24. ( − 6 , 0 ) open negative 6 comma 0 close
25. (0, 5)
26. ( − 11 , − 11 ) open negative 11 comma negative 11 close
27. ( − 8 , 14 ) open negative 8 comma 14 close

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