Question

13
a quadratic function models the height, in feet, of an object above the
ground in terms of the time, in seconds, after the object was launched.
according to the model, the object was launched from a height of 0
feet and reached its maximum height of 1,600 feet 10 seconds after it
was launched. based on the model, what was the height, in feet, of the
object 15 seconds after it was launched?

Explanation:

Step1: Set vertex form of quadratic

The vertex is (10, 1600), so $h(t) = a(t-10)^2 + 1600$.

Step2: Find a using h(0)=0

Substitute t=0, h=0: $0 = a(0-10)^2 + 1600 \Rightarrow 100a = -1600 \Rightarrow a=-16$.

Step3: Compute h(15)

$h(15) = -16(15-10)^2 + 1600 = -16(25) + 1600 = -400 + 1600 = 1200$.

Answer:

1200