Question

The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 4 feet, represented by a vertex of (6,4), and lands 12 feet from the water jet, represented by (12,0). Write a function in vertex form that models the path of the stream.

Answer 1

Answer:

y = -4/36 * (x-6)^2 + 4

Step-by-step explanation:

The  quadratic equation expressed  in vertex from is

y = a(x-h)^2 + k

The vertex is  

Vertex = (h,k) = (6,4)

This means

y = a(x-6)^2 + 4

To find a, we know that at 12 feet from the water jet, the height is equal to zero.

0 = a(12-6)^2 + 4

a = -4/36

Therefore, the equation is

y = -4/36 * (x-6)^2 + 4

Please see attached graph for reference.