Question

You jump off the high dive at a swimming pool. Your

height as a function of time is modeled by
h = 16t² + 12t + 30, where t is the time in
seconds after you jump and h is the height in feet.
What is your maximum height, in feet?

Answer 1

Answer: 33.375 feet

Explanation:

To find the maximum height, we need to find the vertex of the parabolic function h = 16t² + 12t + 30.

The vertex of a parabola with equation y = ax^2 + bx + c is located at x = -b/2a and y = c - b^2/4a.

In this case, a = 16, b = 12, and c = 30.

So,

t = -b/2a = -12/(2*16) = -3/8

h = 16(-3/8)² + 12(-3/8) + 30 = 33.375

Therefore, the maximum height reached is 33.375 feet.