Question

Suppose D(T) = A(T-H)2 +K represents the hieght of an object in feet after T seconds. Suppose an object has a

maximum height of 12 feet after 2 seconds. This same has height of 0 feet after 3 seconds. Create D(T) answers in
exact form.

Answer 1

D(T) = -12(T -2)² +12

Explanation:

You want the quadratic function D(T) = A(T -H)² +K that has a vertex of (2, 12) and goes through the point (3, 0).

Vertex form

The given equation is in vertex form, which mean the maximum (vertex) is (H, K) = (2, 12). The value of A can be found using the other supplied point.

D(3) = 0

D(3) = 0 = A(3 -2)² +12 = A +12 ⇒ A = -12 . . . . . using T=3, (H, K) = (2, 12)

The function D(T) is ...

D(T) = -12(T -2)² +12