# The height, h, in meters, of a football t seconds after being thrown is given by the formula: h = 30t - 5t^2. How long after being thrown is the ball at a height of 25 meters?

Nov 24, 2017

Replace h with 25m.

$25 = 30 t - 5 {t}^{2}$

Rearrange it

$- 5 {t}^{2} + 30 t - 25 = 0$

Facotorization and Simplification

$- 5 \left({t}^{2} - 6 t + 5\right) = 5 \left(t - 5\right) \left(t - 1\right)$

Find t

$\left(t - 5\right) = 0 , t = 5$
$\left(t - 1\right) = 0 , t = 1$

Has a height of 25 at 1 s and 5 s