The function f(t)= -5t^2+20t +60 models the approximate height of an object t seconds after it is launched. how many seconds does it take the objects to hit the ground?

t = 6: It takes 6 seconds for the object to hit the ground

Step-by-step explanation:

So, we need to find t when the height is 0. Since -5t² + 20t + 60 represents the height, that needs to equal 0.

Equation: -5t² + 20t + 60 = 0

Divide by -5: t² - 4t - 12 = 0

Find two numbers that add up to -4t and multiply to -12t²: -6t, 2t

Substitute: t² - 6t + 2t - 12 = 0

Factor: (t - 6)(t + 2) = 0

Answers: t = 6, t = -2

Since time can't be negative, t = 6.

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