My last two posts (Navigating the Shift - Quadratic Explorations and From Side-to-Side - Horizontal Shifts in Quadratic Functions) were ‘how-to’ posts related to helping students understand how vertical and horizontal shifts to the parent quadratic function impact the equation. Recognizing the shifts that have happened can help a student use key points in the graph to write an equation of a quadratic, or the reverse, look at the equation of a quadratic and understand what the graph will look like before they even graph it.
An understanding about the shifts and impact on an equation can be helpful on assessments and the like, but there is that age-old question, “when are we ever going to use this in real life?” that is needed to provide the engagement and relevance for students. Providing context to these shifts helps students see purpose and make connections and, more importantly, actually use what they are learning in a real world situation.
This post is going to provide two different situations - one that is a ‘simulation’ to model how you might use key points to create a quadratic equation and answer some ‘in-context’ questions, and the other is a much more realistic situation that applies the same idea but helps answer questions students might encounter outside of a math class. Both are great ways to engage students and have them apply what they are learning. As always, I have some videos to do the explaining, and use two different calculators - the fx-CG50 color graphing calculator and the fx-991CW scientific calculator with QR functionality for visualization and analysis.
Situation #1 - Flying Fish w/fx-CG50 Prizm graphing calculator.
This is a simulation that uses the CG50’s built in photos/visuals to plot points as a fish jumps from one bowl to another. This is a favorite activity of mine, and while it may not be completely realistic (though if you have ever owned a goldfish, they do jump out of their bowls) but it is an engaging and provides a context to using key points on a parabolic path, that applies understanding of the quadratic shifts, to create a quadratic equation and see how well the they ‘fit the curve’. The video shows how to do the activity and the attached PDF is the activity (with steps) that you can use with your students.
Situation #2 - Olympic Diver w/fx-991CW
The 2024 Summer Olympics just finished and these sports and statistics can provide great context to mathematical concepts. Looking at the high-dive event, where divers are jumping from a 10 m platform creates a nice real-world context for quadratics. A very simple start might be to provide students with the height/second of a diver and have them use what they know about the shifts of a parent function to try to model the path and determine the equation.
The table below represents the height/second of an Olympic diver, jumping from a 10 m platform. This video below shows how to use the fx-991CW’s table menu and QR functionality to explore the points and apply an understanding of the shifts to a parent function to make sense of the data. The context allows them to make sense of the data and ask questions, which then leads to a more in-depth understanding of how the quadratic function can provide information for real-world situations.
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