# Engaging students: Graphing parabolas

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Cody Luttrell. His topic, from Algebra: graphing parabolas.

How can this topic be applied in your studentsâ€™ future courses in mathematics or science?

Understanding the graph of a parabola will be very important in an Algebra 1 students future math and science classes. When a student enters Algebra II, they will be dealing with more complicated uses dealing with quadratic functions. An example would be complex numbers. When dealing with a parabola that does not cross the x-axis, you will end up with an imaginary solution, but if the student does not understand the graph of a parabola they may not understand this topic. When the student reaches pre-calculus, understanding the transformations of a parabola will aid when dealing with transformations of other functions such as cubic, square root, and absolute value.
Understanding the graph of a parabola will benefit a student in Physics when they deal with equations of projectiles. Knowing that there is symmetry in a parabola can aid in knowing the position of the projectile at a certain time if they know the time the projectile is at its maximum height.

How has this topic appeared in high culture (art, classical music, theatre, etc.)?

The shape of the parabola is used constantly in art and even architecture. A quick engage that I can have for the students would be a powerpoint of photos of parabolas in the real world. Examples would include arches in bridges, roller coasters, water fountains, etc. Ideally, I would want my students to see the pattern that I am getting at and see the parabola in all of these objects. I could then ask the students to brainstorm where else they can find this shape. I would expect to hear answers such as the St. Louis Arch, the sign at McDonalds, or even a rainbow.
After learning about quadratics, we could come back to the topic of architecture and parabolas. After they have learned about the transformations of parabolas, we can discuss how to make arch longer or shorter in bridges(if it follows the parabolic shape). We could also discuss how if we wanted to make a bridge taller, how it would affect the distance between the legs of the bridge.

Using Technology.

A great video from Youtube to show the students to introduce them to graphing parabola: https://www.youtube.com/watch?v=E_0AHIaK48A

In the video, it shows how parabolas are even used in famous videogames such as Mario Bros. In the video, you see a few clips of Mario and Luigi jumping over enemies. The video outlines the path that he jumped and you can notice that it is in the shape of a parabola. The video then goes into explanation that Mario if following the path of y=-x^2. After this explanation, the video switches to Luigi. When Luigi jumps, he also follows the form of a parabola, but slightly different then the way Mario jumps. Luigi can jump higher than Mario, but not as far. The video then states that Luigi is following the path of y=-1.5x^2. This can introduce the idea of compression and stretches. The video than continues on with other examples of how parabolas are used within the game such as vertical shifts.

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