Question

Ben shoots an arrow. The height of

the arrow can be modeled by
y = -16x² + 100x + 4, where y.
represents the height in feet of the
arrow x seconds after it is shot into
the air. What is the maximum
height of the arrow and when did it
reach the maximum height?

Answer 1

Answer: The maximum height of the arrow is the vertex of the parabola. To find this, we can set the derivative of the function equal to zero and solve for x.

y' = -32x + 100

Setting y' = 0 and solving for x:

0 = -32x + 100

32x = 100

x = 100/32

So the arrow reaches its maximum height of y = -16(100/32)² + 100(100/32) + 4 = 100 feet at x = 100/32 seconds after it is shot into the air.

Explanation: