Emilio throws a marshmallow into the air from his balcony. the height of the marshmallow (in feet) is represented by the equation h=−16t2+8t+48, where t is the time (in seconds) after he throws the marshmallow. how long does it take the marshmallow to hit the ground, where h=0?

Step-by-step explanation:

The height of the marshmallow (in feet) is represented by the equation h=−16t2+8t+48,

where t is the time (in seconds) after he throws the marshmallow.

The equation is a quadratic equation. When the marshmallow hits the ground, its height from the ground will be zero. Therefore

−16t^2+8t+48 = 0

- 2t^2 + t + 6 = 0

Multiplying through by the negative sign. It becomes

2t^2 - t - 6 = 0

2t^2 + 3t - 4t - 6 = 0

t(2t + 3) - 2(2t + 3) = 0

(t - 2)(2t + 3) = 0

t - 2 = 0 or 2t + 3 = 0

t = 2 or t = - 3/2

The time cannot be negative

So it will take 2 seconds to hit the ground