Out of Left Field
From which MLB ballpark is it hardest to hit a home run?
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.Common Core Standards
Content Standards
Mathematical Practices
Downloads
Additional Materials
- Graphing technology (optional)
Shoutouts
Major League Baseball, David Ortiz
Related Lessons
Datelines
What's an acceptable dating range? Students use linear equations and linear inequalities to examine the May-December romance, and ask whether the Half Plus Seven rule of thumb is a good one.
Carpe Donut
How much should people pay for donuts? Students use linear, rational, and piecewise functions to describe the total and average costs of an order at Carpe Donut.
Canalysis
What's the ideal size for a soda can? Students use the formulas for surface area and volume of a cylinder to design different cans, calculate their cost of production, and find the can that uses the least material to contain a standard 12 ounces of liquid.
Sofa Away From Me
How far away from the TV should you sit? Students use right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.
Loan Ranger
How much do you really pay when you use a credit card? Students develop an exponential growth model to determine how much an item really ends up costing when purchased on credit.
Fall of Javert
Could Inspector Javert have survived the fall? Students use quadratic models to determine how high the bridge was in Les Misérables, and explore the maximum height from which someone can safely jump.
Going Once, Going Twice - Legacy Version
How much should you bid in an auction? Students use probability, expected value, and polynomial functions to develop a profit-maximizing bidding strategy.
iPod dPreciation
How has the iPod depreciated over time? Students compare linear and exponential decay, as well as explore how various products have depreciated and what might account for those differences.
Bracketology
What’s the best strategy for creating a March Madness bracket? Students use probability to discover that it’s basically impossible to correctly predict every game in the tournament. Nevertheless, that doesn’t stop people from trying.
Siren Song
Does the same sound always sound the same? Students come up with equations in several variables to explore the Doppler Effect, which explains how sound from a moving object gets distorted.
Green Acres
How has the urban population changed over time, and will we all eventually live in cities? Students use recursive rules along with linear and exponential models to explore how America's urban areas have been growing over the last 200 years.
Wiibates
How much should Nintendo charge for the Wii U? Students use linear functions to explore demand for the Wii U console and Nintendo's per-unit profit from each sale. They use those functions to create a quadratic model for Nintendo's total profit and determine the profit-maximizing price for the console.
Pizza Pi (HS)
Which size pizza should you order? Students apply the area of a circle formula to write linear and quadratic formulas that measure how much of a pizza is actually pizza, and how much is crust.
Icy Hot (HS)
How have temperatures changed around the world? Students use trigonometric functions to model annual temperature changes at different locations around the globe and explore how the climate has changed in various cities over time.
Prescripted
How should pharmaceutical companies decide what to develop? In this lesson, students use linear and quadratic functions to explore how much pharmaceutical companies expect to make from different drugs, and discuss ways to incentivize companies to develop medications that are more valuable to society.
Connected
Do social networks like Facebook make us more connected? Students create a quadratic function to model the number of possible connections as a network grows, and consider the consequences of relying on Facebook for news and information.
Pandemic
Why hasn't everyone already died of a contagion? And, if vampires exist, shouldn't we all be sucking blood by now? Students model the exponential growth of a contagion and use logarithms and finite geometric series to determine the time needed for a disease to infect the entire population.
Second Degree
How dangerous are heat and humidity? Students use polynomial functions to explore the heat index and discuss the life-and-death consequences that cities around the world will face in the coming years.
Mercury Rising
How have temperatures changed around the world? Students use periodic functions to compare long-term average monthly temperatures to recorded monthly temperatures, evaluate evidence of climate change, and discuss possible consequences.