B Apply

Determine whether a quadratic model exists for each set of values. If so, write the model.

18. f ( − 2 ) = 16 , f open negative 2 close equals 16 comma  f(0) = 0, f(1) = 4
19. f(0) = 5, f(2) = 3, f ( − 1 ) = 0 f open negative 1 close equals 0
20. f ( − 1 ) = − 4 , f ( 1 ) = − 2 , f ( 2 ) = − 1 f open negative 1 close equals negative 4 comma f open 1 close equals negative 2 comma f open 2 close equals negative 1
21. f ( − 2 ) = 7 , f open negative 2 close equals 7 comma  f(0) = 1, f(2) = 0

22. 1. Geometry Copy and complete the table. It shows the total number of segments whose endpoints are chosen from x points, no three of which are collinear.

       Number of points, x	2	3	□ white square	□ white square
       Number of segments, y	1	3	□ white square	□ white square

    2. Write a quadratic model for the data.
    3. Predict the number of segments that can be drawn using 10 points.

23. Think About a Plan The table shows the height of a column of water as it drains from its container. Use a quadratic model of this data to estimate the water level at 30 seconds.

    Water Levels

    Elapsed Time (s)	Water Level (mm)
    0	120
    20	83
    40	50

    • What system of equations can you use to solve this problem?
    • How can you determine if your answer is reasonable?
24. A parabola contains the points ( − 1 , 8 ) , open negative 1 comma 8 close comma  (0, 4), and (1, 2). Name another point also on the parabola.

25. 

    1. Postal Rates Find a quadratic model for the data. Use 1981 as year 0.

       Price of First-Class Stamp

       Year	1981	1991	1995	1999	2001	2006	2007	2008
       Price (cents)	18	29	32	33	34	39	41	42

       Source: United States Postal Service

    2. Describe a reasonable domain and range for your model. (Hint: This is a discrete, real situation.)
    3. Estimation Estimate when first-class postage was 37 cents.
    4. Use your model to predict when first-class postage will be 50 cents. Explain why your prediction may not be valid.

26. Road Safety The table below gives the stopping distance for an automobile under certain road conditions.

    Speed (mi/h)	20	30	40	50	55
    Stopping Distance (ft)	17	38	67	105	127

    1. Find a linear model for the data.
    2. Find a quadratic model for the data.
    3. Writing Compare the models. Which is better? Explain.
27. Open-Ended Write three different quadratic functions, each with a graph that includes (0, 0) and ( 5 , − 1 ) . open 5 comma negative 1 close .

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