Precalc fountain question

Question

fountain 1 has a water jet that sprays water from a location on a wall 12ft above the ground. The water reaches it's maximum height at a point 20 ft above ground and 4 ft from the wall. Write a function to model the path of the water. Show your work and define the variables

Answer 1

The path of the water jet is parabolic with quadratic equation given in vertex from as

y = a(x-h)² + k

 Assume the wall lies along the Y axis, and the ground is along the x- axis.

Since the maximum height occurs at 4 feet from the wall, and 20 feet above the ground, then h = 4, k = 20.

Y = a(x - 4) ² + 20.

To solve for a, note that when x = 0, y = 12.

∴ 12 = a (0 - 4)² + 20  ⇒ a = - 0.5

The equation is therefore

y = -0.5(x - 4)² + 20