The equation y = - 2x2 + 6x + 36 represents the height of a projectile over time, where y represents the height, in feet, and x represents the time, in seconds. After how many seconds will the projectile hit the ground?

6 seconds

Step-by-step explanation:

Given

y = - 2x² + 6x + 36

When the projectile hits the ground the height y = 0, thus

- 2x² + 6x + 36 = 0 (divide through by - 2)

x² - 3x - 18 = 0 ← in standard form

(x - 6) (x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 3 = 0 ⇒ x = - 3

However x > 0 ⇒ x = 6

The projectile takes 6 seconds to hit the ground.