factoring word problem

Question

A ball is projected upward from ground level. After t seconds, its height in feet is a function defined by f(t) = -16t^2+80t. After how many seconds will it reach a height of 96 ft?

Answer 1

96 = -16t² + 80t ⇔ 16t² - 80t + 96 = 0 ⇔ t² - 5t + 6 = 0 ⇔ ( t - 3)( t - 2 ) = 0

 

t = 3 seconds ; Check -144 + 240 = 96 ft

 

t = 2 seconds ; Check  -64 + 160 = 96 ft

 

The ball will reach height 96 ft 2 seconds after being projected, during the ascending motion AND a second later in the descending motion.