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The height, y m, of a baseball above the ground x seconds after it has been hit is given by y = -5x^2 + 20x + c, where c is a constant.

 

 Feb 27, 2021
 #1
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This equation is a dome shaped parabola     maximum will occur at the vertex

  the roots of the equation should be = and at the vetex for the max value

 

    this will require that the discriminant = 0

 

50 > -5x^2 + 20x + c

-5x^2 + 20 x   + c-50  < 0

    find when discr = 0

        20^2 - 4(-5)(c-50)  = 0

           400 + 20c - 1000 = 0

                     20c =  600

                         c = 30   max for fxn to = 50            so c<30

 

y = -5x^2 +20x + 20

       -5 ( x^2 -4)    + 20

       -5 ( x -2)2       +20 + 20 

  y=   - 5 ( x-2)^2   + 40

 

You can do part iii

 Feb 27, 2021

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