Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Find an equation in standard form of the parabola passing through the points.

7. ( 1 , − 2 ) , ( 2 , − 2 ) , ( 3 , − 4 ) open 1 comma negative 2 close comma open 2 comma negative 2 close comma open 3 comma negative 4 close
8. ( 1 , − 2 ) , ( 2 , − 4 ) , ( 3 , − 4 ) open 1 comma negative 2 close comma open 2 comma negative 4 close comma open 3 comma negative 4 close
9. ( − 1 , 6 ) , open negative 1 comma 6 close comma  (1, 4), (2, 9)
10. (1, 1), ( − 1 , − 3 ) , ( − 3 , 1 ) open negative 1 comma negative 3 close comma open negative 3 comma 1 close
11. ( 3 , − 6 ) , ( 1 , − 2 ) , open 3 comma negative 6 close comma open 1 comma negative 2 close comma  (6, 3)
12. ( − 2 , 9 ) , ( − 4 , 5 ) , open negative 2 comma 9 close comma open negative 4 comma 5 close comma  (1, 0)

13. x	f(x)
    − 1 negative 1	− 1 negative 1
    1	3
    2	8

14. x	f(x)
    − 1 negative 1	17
    1	17
    2	8

15. x	f(x)
    − 1 negative 1	− 4 negative 4
    1	− 2 negative 2
    2	− 4 negative 4

    See Problems 2 and 3.

16. Communications The table shows the percent of houses with cable TV in a city.

    Cable Television Access

    Year	1985	1990	1995	2000	2005
    % of Households	46	59	66	68	69

    1. Find a quadratic model using 1985 as year 0, 1990 as year 5, and so on.
    2. Use the model to estimate the percent of households with cable TV in 1998.

17. Physics A man throws a ball off the top of a building and records the height of the ball at different times, as shown in the table.

    Height of a Ball

    Time(s)	Height (ft)
    0	46
    1	63
    2	48
    3	1

    1. Find a quadratic model for the data.
    2. Use the model to estimate the height of the ball at 2.5 seconds.
    3. What is the ball's maximum height?

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