Projectile Motion: Quadratic equations are used to model the trajectory of an object in projectile motion.

A ball is thrown upward with an initial velocity of 10 m/s from a height of 5 meters. The height $h$ of the ball after $t$ seconds is given by the equation

h(t) = -5t² + 10t + 5

Find the time when the ball hits the ground

Factor the function. We can factor out a -5 from each component

h(t) = -5(t² – 2t – 1) = 0

0 = t² – 2t – 1

0 = (t – 2)(t + 1)

solve for t

t = 2 and -1

Since time cannot be negative, the answer is 2

t = 2 seconds