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18 April, 16:34

Elena is the champion diver on her swim team. She dives from a diving board that is 48 feet high. Her position in the pool is represented by the function h (t) = - 16t^2+24t+40, where t represents time in seconds and h (t) represents height in feet.

Part A: After how many seconds does Elena enter the pool?

Part B: What is the greatest height Elena reaches her dive?

Part C: How long will it take Elena to reach the maximum height?

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  1. 18 April, 16:47
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    A. enter pool is when h (t) = 0

    B. max height is the vetex

    C. that is the t value of the vertex

    A.

    0=-16t²+24t+40

    using math

    t=-1 or 5/2

    can't be negative time

    t=5/2

    after 2.5 seconds

    B. find vertex

    get into form

    y=a (x-h) ^2+k

    complete the square

    h (t) = - 16t²+24t+40

    h (t) = (-16t²+24t) + 40

    h (t) = - 16 (t²-1.5t) + 40

    h (t) = - 16 (t²-1.5t+0.5625-0.5625) + 40

    h (t) = - 16 ((t-0.75) ²-0.5625) + 40

    h (t) = - 16 (t-0.75) ²+9+40

    h (t) = - 16 (t-0.75) ²+49

    vertex is at t=0.75 and h (0.75) = 49

    A. after 2.5 seconds

    B. 49ft

    C. 0.75 seconds
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