How to solve functions

Question

NASA launches a rocket at  seconds. Its height, in meters above sea-level, as a function of time is given by . Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after  seconds. How high above sea-level does the rocket get at its peak? 

The rocket peaks at

  meters above sea-level.

Answer 1

h(t) = -4.9t² + 229t + 318

It splashes down when h(t) = 0. Set h(t) = 0 and solve for t using the quadratic formula. You will get a negative and a positive value for t. The positive value is the correct solution.

Maximum height occurs at the vertex of the height-vs.-time parabola, which is at

t = -b/(2a),

where

b = 229

a = -4.9

Evaluate h(t) at this value of t to get h_max.