Interpreting nonlinear expressions

Question

h(x)=−5(x−1)²+7

The height, h, of a stream of water, in feet above the surface, in a fountain at a horizontal distance of x feet from the nozzle, is given by the function shown above. What is the best interpretation of the number 7 in the function?

Answer 1

The 7 is the y-coordinate of the vertex of the parabola described by h(x). I will use y for the height to avoid confusing height with the symbol h used for the x-coordinate of the vertex.

y = a(x - h)² + k

The vertex is the point (h,k), so you can see why the 7 in the given equation is the y-coordinate of the vertex of the parabola described by the given function.