A football is kicked and follows a path given by [math]y = –0.03(x – 30)^2 + 27[/math], where [math]y[/math] represents the height of the ball in feet and [math]x[/math] represents the ball’s horizontal distance in feet. What is the maximum height the ball reaches? What horizontal distance maximizes the height? What are the zeros of the function? What do the zeros represent in the context of the problem? What is the total horizontal distance the ball travels? If the ball reaches a height of [math]20.25[/math] feet after traveling [math]15[/math] feet horizontally, will the ball make it over a [math]10[/math]-foot-tall goal post that is [math]45[/math] feet from the kicker?
[list=1] [*]Determine the maximum height of the ball. [*]Determine the horizontal distance of the ball when it reaches its maximum height. [*]Determine the zeros of the function. [*]Determine what the zeros represent in the context of the problem. [*]Determine the total horizontal distance the ball travels. [*]Determine whether the ball will clear the goal post. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCGPS Analytic Geometry[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.