Algebra-I think you use quadratic formula

wallee

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Apr 20, 2008
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A ball is thrown from a platform. The height in feet above the ground after t seconds is given by the equation h(t)= -16t square + 32t +20. How many seconds will pass until the ball reaches its maximum height?

I tried using the quadratic formula:


but got -0.5 and 2.5. The answer in the book is 1. I am confused.
 

galactus

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The max height is at the vertex of the parabola. To find that value you can use \(\displaystyle t=\frac{-b}{2a}=\frac{-32}{2(-16)}=1\)
 

masters

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Mar 30, 2007
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If you don't know where Galactus got his -b/(2a) expression, you may understand this:

The max value of your parabola is the x-coordinate of the vertex.

The x-coordinate of the vertex is the midpoint of the x-intercepts.

You found the x-intercepts to be -.5 and 2.5.

Using the midpoint formula: (-.5 + 2.5)/2 = 1

So, 1 is the x-coordinate of the vertex and the max value of the parabola.

BTW, if you want to derive the -b/(2a) expression, you'd have to add the two parts of the quadratic formula together and divide by 2. It's much simpler to memorize -b/(2a).
 
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