A thrown ball hits the ground and one of its bounces follows the parabolic path given by
y = -2/9x^2 + 52/9x - 320/9
where x is the horizontal distance (in feet) and y is the corresponding height (in feet). What is the maximum height that the ball reaches on this bounce?

Question

A thrown ball hits the ground and one of its bounces follows the parabolic path given by
y = -2/9x^2 + 52/9x - 320/9 
where x is the horizontal distance (in feet) and y is the corresponding height (in feet). What is the maximum height that the ball reaches on this bounce?

anonymous · Answer

the maximum height occurs at the vertex of the parabola... the x-coordinate of the vertex is given by x=-b/(2a) where b is your x coefficient and a is your x^2 coefficient.

to get the height, just plug this x coordinate back in to y = and simplify...