I created this image because it will be useful for my Algebra 1 class. I will show this image to my students at the beginning of the chapter on graphing quadratic functions. I think that my students will enjoy this because the boy in the image is one of their freshman classmates (he's also my son).
I will ask the boys to focus on the actual parabola. I will ask first what they notice about it. What is the shape of it - is it opening upward or downward? Where does it intercept the y-axis? How many times does it intercept the y-axis? Where does it intercept the x-axis? How many times does it intercept the x-axis? Does it have a highest or lowest point, and if so, what is it? Is it symmetric? What does the equation for this parabola look like?
Toward the end of the chapter, when the students have learned how to graph quadratics, I will show the image again. Hopefully, this time they will be able to give more information about the quadratic equation.
What a great idea! You could bring many different kinds of real-world shapes into a graph. This would probably be a much more memorable experience than just showing a parabola.
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