Question

The path of a soccer ball is modeled by the function h(x) = -0.005x2 + 0.25x, where h is the height in meters and x is the horizontal distance that the ball travels in meters. What is the maximum height that the ball reaches? ___________ m.

Answer 1

Using calculus or a formula?

Answer 2

formula

Answer 3

3.125 m

Answer 4

The general formula (derived using calculus however) for the turning point of a quadratic function (in the form ax^2 +bx + c) is \[\frac{ -b }{ 2a }\]
That will give you the time when the ball is at it's maximum height...
To solve for the height, plug the time back into the original function!

Answer 5

that is suppose to read
\[h(x)=-0.005x^2 + 0.25x\]
right?