Question

The function f(t) = −5t 2 + 20t + 60 models the approximate height of an objectt seconds after it is launched. How many seconds does it take the object to hit theground?

Answer 1

Please, use " ^ " to indicate exponentiation: f(t) = −5t^2 + 20t + 60.

When the object hits the ground, f(t) = 0 = −5t^2 + 20t + 60

We must solve this quadratic equation for t. Start by dividing all 4 terms by -5:

t^2 - 4t - 12 = 0. Factoring, we get (t-6)(t+2)=0. Thus, t=6. Omit t=-2.

How many seconds does it take the object to hit the ground? 6 seconds.