A sports science consultant was hired to analyze the throwing arm of our star outfielder. It was determined that the ball was thrown a distance of 100 feet, at a peak height of 40 feet.[br][br]Find a formula (a function [b][math]h(x)[/math][/b]) that gives the height of the ball as a function of the distance from the outfielder, by transforming the parent function [math]f(x)=x^2[/math] (shown in dashed blue).

A ball thrown on Planet Earth follows a parabolic trajectory due to gravity. That is, the path of the ball is a parabola. The parent function for a parabola is [math]y=x^2[/math], but clearly this by itself does not properly describe the path of the ball.[br][br]To turn a parent function into something useful for modeling real life, we can apply transformations. Transformations stretch and shift a graph to make the parent function's shape "fit" the real-life scenario.[br][br]Adjust the sliders to transform parent function [math]f(x)=x^2[/math] into a model for the throw, which we'll call [math]h(x)[/math].