please help!!!!?

Question

A baseball is hit at a point 3 feet above the ground at a velocity of 100ft/s and at an angle of 45 degree with respect to the ground. The path of the baseball is given by the function: f(x) = -0.0032x^2 + x+ 3, where f(x) is the height of the baseball(in feet) and x is the horizontal distance from home plate(in feet_. What is the maximum height reached by the baseball?

please explain as you're solving, thank you

Answer 1

f(x) = -0.0032x^2 + x+ 3

This is a quadratic and the coefficient of x^2 is negative, so it has a maximum at x = -b/2a = -1/2(-0.0032) = 156.25.

The maximum value is f(156.25) = -0.0032(156.25)^2 + 156.25 + 3 = 81 feet to the nearest foot.