Watching a home run arc through the air and into the crowd is a thing of beauty. But is it easier to hit home runs in some parks, and harder in others? After all, the left field wall in Fenway, for example, is more than four times taller than the wall in Yankee Stadium!

In this lesson, students find the roots and maxima of quadratic functions to model the trajectory of a potential home-run ball. They also come up with the equation of an “average” home run into left, and use that equation to explore whether some parks are friendlier towards hitters than others.

Students will

Find the maximum height and distance of a baseball by identifying the vertex and roots of a quadratic function

Determine which of three hypothetical trajectories would be a home run at Fenway Park

Explore whether a home run at Fenway will necessarily be a home run in other ballparks

Given the average maximum height and distance, derive a formula for the trajectory of an average home run hit into left field

Use data on different ballparks to determine whether it’s easier to hit home runs in some parks over others

Consider reasons why the trajectory of a baseball might not actually be parabolic

Before you begin

Students should have some previous experience with quadratic functions. The vertex form of a quadratic function is used throughout this lesson (y = a(x — h)^{2} + k), so some previous exposure to this way of writing a quadratic equation will be helpful. Students will also need to use the quadratic formula to find the roots of a quadratic function.

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