A ball in flight is modeled by the function h(t)=-16t²+128t. Find the maximum height and time to get there.

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A ball in flight is modeled by the function h(t)=-16t²+128t. Find the maximum height and time to get there.

Mathematics
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The maximum height will be the y coordinate of the vertex. Can you find that?
huh?
Do you know that the graph of that function is a parabola?

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yes
So then you know that it has either a high point or a low point?
yes
which one does this problem have...a high point (maximum) or a low point (minimum)?
maximum
It has a hight point (maximum) because the coefficient of the t^2 term is negative.
Do you know that the high point is called the vertex?
yes
Do you know that the vertex is represented by an ordered pair that has an x value and a y value?
yes
Ok. we need to find that highest point (vertex). The x coordinate of the vertex is x=-b/2a Calculate that.
\[x=\frac{-128}{2(-16)}=\frac{-128}{-32} = 4\]
\[y=-16(4)^2+128(4)= 256\]
So the vertex is (4,256) and the maximum height of the ball is 256 feet.
And that happens when the time is 4 seconds.

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