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Thread: quadratic function problem solving

  1. #1
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    Post quadratic function problem solving

    I to solve a problem, I solved 2 out of 3 questions now I'm stuck. Sorry if it's not well written, I translated from french.
    During a basketball game, Mary throws the ball in the basket. The trajectory of the ball can be represented by the equation h = -0,078d^2 + 0,92d + 2

    question: What is the maximum height the ball can reach

    I've tried finding the vortex because that seems to make sense in this context but it gives me an answer like -0,78m. This doesn't make sense because it's negative and in the previous question I found that the initial height of the ball is 2m, the maximum height can't be lower than the initial height.
    thanks
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  2. #2
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    Re: quadratic function problem solving

    max height, $h$, occurs at the vertex of the parabola's graph

    for $f(x)=ax^2+bx+c$ with $a < 0$, $\implies f_{max} = f\left(-\dfrac{b}{2a}\right)$
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  3. #3
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    Re: quadratic function problem solving

    I suspect you dropped a negative sign somewhere- probably in the leading coefficient, -0.078.

    It would help if you showed exactly what you did.
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  4. #4
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    Re: quadratic function problem solving

    $h=-0.078d^2+0.92d+2$

    $h'=-0.0782d+0.92$

    $h'=0=-.156d+0.92$

    $d=\dfrac{0.92}{1.56}$

    $d=\dfrac{92}{156}=\dfrac{46}{78}=\dfrac{23}{39}$

    $h=-0.078(\frac{23}{39})^2+0.92(\frac{23}{39})+2$

    $=-0.027+0.54+2$

    $=2.52$
    Last edited by deesuwalka; Feb 17th 2017 at 02:43 AM.
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