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:
