Path of a ball- Quadratics Word Problem

Question

A ball is thrown across a playing field. Its path is given by the equation y=-0.005x^2 +x+5 where x is the distance the ball has traveled horizontally and y is its height above ground level, both measured in feet. What is the maximum height attained by the ball? How far has it traveled horizontally when it hits the ground?

Answer 1

For the parabola -ax²+bx+c = 0, the max height will be the vertex at x = b/2a (I have forced a to be positive in order to stress that this is a downward facing parabola with a maximum height at the vertex)

In this case, the max will occur at 1/(.005*2) = 100

Find max height by plugging in the x.

You can find the displacement for y=0 by using the quadratic formula for x.