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26 April, 19:07

Challenge A baseball player hits a baseball and its height is modeled by the function h (t) = - 16t^2=12t+4. If t represents time, in seconds, find the time in seconds when the ball hit the ground

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  1. 26 April, 20:17
    0
    That is when height or h (t) = 0

    0=-16t^2+12t+4

    use math to solve

    I will complete the square

    group t terms

    0 = (-16t^2+12t) + 4

    factor out quadratic coefient

    0=-16 (t^2 - (3/4) t) + 4

    take 1/2 of linear coefient and squaer it

    (-3/4) / 2=-3/8, (-3/8) ^2=9/64

    take negative and positive of it and add to inside of parenthasees

    0=-16 (t^2 + (-3/4) t+9/64-9/64) + 4

    factor pefect square

    0=-16 ((t-3/8) ^2-9/64) + 4

    expand/distribute

    0=-16 (t-3/8) ^2+9/4+4

    0=-16 (t-3/8) ^2+25/4

    add - 16 (t-3/8) ^2 to both sides

    16 (t-3/8) ^2=25/4

    divide both sides by 16

    (t-3/8) ^2=25/64

    sqrt both sides

    remmber positive and negative roots

    t-3/8=+/-5/8

    add 3/8 to both sides

    t=3/8+/-5/8

    t=3/8+5/8 or t=3/8-5/8

    t=8/8 or t=-2/8

    t=1 or - 1/4

    we can't have negative time so

    at t=1

    1 second
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