## 1 thought on “Parabola”

1. Ezra Halleck

This submission is pretty close to what I was expecting as far as using desmos to get a graph which approximates the curve photographed. Good job! The origin has been placed at the vertex and since the parabola is upside down, the equation will be y=-a*x^2 where a is some positive number. However, with an enlarged picture, it would be more evident that a rainbow is in fact an arc (part of a circle). [You can see the entire circle in halos, which have similar optics to rainbows.] For further study, after enlarging the picture (or zooming in), superimpose the equation of a circle simultaneously with that of parabola. Use y=sqrt(r^2-x^2)-r, where r is the radius. The top of the circle would coincide with the origin. I am guessing that this would show that the circle is a better fit. When doing this, just use one color, say yellow. [In your superimposition, notice that your curve starts at one end of the spectrum (red) and goes to the other (violet).]