Quadratic Equation

Question

Suppose the valley following the lift hill is in a shape of a parabola that has a maximum drop of 14m and the start and end points are 20m apart. Write a quadratic equation that models the profile of this valley.  The starting point will be at (32,16)

Answer 1

(32,16) and (12,16) are end points

vertex = (22,2)

an upward opening parabola with minimum point = vertex

32-20=12

22 = average of 32 and 12

y=(x-22)^2 + 2 is the parabola's equation in vertex form

or if measured in the other direction

endpoints are (32,16) and (52, 16)

with vertex = (42,2)

then equation is

y=(x-42)^2+ 2