Answer:
D(T) = -12(T -2)² +12
Step-by-step 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
