# Real Life Parabola

The real life parabola that i have chosen is The St.Louis Arch. It is a parabola that goes upward then ends up curving back downwards. Parabolas like these are common in many places.

## 1 thought on “Real Life Parabola”

1. Ezra Halleck

Yes, the link does work. However, I would have pasted in another picture rather than relying on people to copy paste the link into another browser tab. One issue is to get a sense the units. Your equation is y=-x^2. What are the units?

One other thing I should point out is that the St. Louis arch is not a parabola but instead is a catenary. The difference is that best illustrated by a cable or chain. If the chain does not have a load on it, it is a catenary. In a bridge, the main cables do have loads on them, so that the parabola does model the situation better. To get the equation for the upside down catenary whose top is the origin, it is y=-a(b^x+b^-x)+2a. Notice that there are 2 parameters a and b. You could create sliders for a and b, so that you can find which values give you a good fit.

Update: after several hours of fussing, I found out from the wikipedia article, that the equation for a catenary can be created using just one parameter: y=-b/2(e^(x/b)+e^(-x/b))+2b. In desmos, I have superimposed both the parabola that Brian provided together with this one-parameter catenary. I moved sliders to try and get good fits. As you can see, catenary does give a much better fit.