Question

A diver jumps into a pool from a board ten feet above the surface of the water. Her height, h, at any time t seconds after jumping is given by the equation h = t squared - 8t + 10. What is the minimum height that she reaches? (Note: Negative values of h mean the diver is below the water.)

A.
–26 feet

B.
–10 feet

C.
–6 feet

D.
–4 feet

Answer 1

First find the vertex of the parabola h(t) = t^2 − 8t + 10. The time of the vertex is t = −b/(2a) = 8/2 = 4 seconds.

h(4) = 4^2 − 8·4 + 10 = 16 − 32 + 10 = −6.

So the minimum height is −6 feet (6 feet below the water). Answer: C.