The height of the baseball in meters t seconds after it is hit is given by the quadratic function h left parenthesis t right parenthesis equals negative 4.9 t

Question

The height of the baseball in meters t seconds after it is hit is given by the quadratic function h left parenthesis t right parenthesis equals negative 4.9 t squared plus 24.5 t plus 1h(t)=−4.9t2+24.5t+1. How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?

Answer 1

The vertex of the parabola will give you the time and the maximum height.

x = -b/2a

h(t) = -4.9t² + 24.5t + 1

t = -24.5/-9.8 = 2.5 seconds

h(2.5) = -4.9(2.5)² + 24.5(2.5) + 1

h(2.5) = -30.625 + 61.25 + 1

h(2.5) = 31.625 meters

V(2.5,31.625)