# Jim held a firehose whose spray formed a parabola that spanned 20m. The maximum height of the spray is 16m. What is the quadratic equation that models the path of the spray?

##### 1 Answer

graph{-0.16x^2+3.2x [-4.41, 27.63, 1.96, 17.98]}

#### Explanation:

Assuming Jim is standing at the point (0,0) facing to the right, we are told that the two intercepts (roots) of the parabola are at (0,0) and (20,0). Since a parabola is symmetrical, we can infer that the maximum point is in the middle of the parabola at (10,16).

Using the general form of the parabola:

Product of roots =

Sum of roots =

We are given a third equation from the maximum point:

When x=10, y=16, i.e.

Since

by subtraction:

therefore:

Returning to our general form of the quadratic equation: