Question

The height of a projectile in feet at time t is determined by the equation h=-16t^2+128t+320. At what time will the projectile be 560 feet high

Answer 1

At 3 seconds and again at 5 seconds

Explanation:

h = -16t² + 128t + 320

560 = -16t² + 128t + 320

16t² - 128t + 240 = 0

t² - 8t + 15 = 0

t² - 5t - 3t + 15 = 0

t(t - 5) - 3(t - 5) = 0

(t - 5)(t - 3) = 0

t = 3, t = 5

Answer 2

3 seconds and 5 seconds

Explanation:

Let the function equal 560 ft

560=-16t^2+128t+320

Subtract 560 from each side

560-560=-16t^2+128t+320-560

0 =-16t^2+128t-240

Divide each side by -16

0/-16 = (-16t^2+128t-240)/-16

0 = t^2 -8t-15

Factor

0=(t-5)(t-3)

Using the zero product property

t-5 =0 t-3=0

t=5 t=3