Question

If a projectile is fired straight upward from the ground with an initial speed of 128 feet per​ second, then its height h in feet after t seconds is given by the function ​h(t)=-16t+128t.

Find the maximum height of the projectile.

The maximum height of the projectile is : _________

Answer 1

256 ft

Explanation:

You want the maximum height of a projectile whose height is given by ...

h(t) = -16t² +128t

Vertex

The equation can be written in vertex form like this.

h(t) = -16(t² -8t)

h(t) = -16(t² -8t +16) +16(16) . . . . . complete the square

h(t) = -16(t -4)² +256

The vertex of the graph of the equation is (t, h) = (4, 256).

The maximum height of the projectile is 256 feet.

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Additional comment

The vertex form equation of a parabola is y = a(x -h)² +k. The vertex coordinates are (h, k).

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