quadratic question

Question

If air resistance is ignored, a projectile such as a rifle bullet or a cannonball follows a parabolic path. Suppose a cannonball fired from the origin follows the graph
y = x − 0.0005x2,
where both x and y are measured in feet.

What is the maximum height the cannonball reaches?

ft

Answer 1

y = -0.0005x² + x

 

Maximum height is at the vertex of this concave-down parabola.  The vertex is at

 

x = -1/[2(-0.0005)] ft = ? ft

 

The maximum height is the function y(x) evaluated at the x computed above.  You should be able to finish from here.