The function h ( t ) = − 3t 2 + 12 t + 63 models the flight of a ball t seconds after it is thrown. When can the ball be expected to hit the ground

As the ball hits the ground, its height will be equal to 0, so...

-3t² + 12t + 63 = 0

t² - 4t - 21 = 0

Using the Viet's theorem to solve the quadratic equation quicker:

t₁ + t₂ = 4

t₁t₂ = -21

t₁ = -3 - this is not possible because time can't be negative

t₂ = 7

That means, the ball is expected to hit the ground after 7 sec has passed.