Problem 2.        Worksheet 9:   The St. Louis Arch and Related Functions

Here is a shifted arch function and its plot:

1. Find a quadratic function f(x) that has the same x-intercepts and the same peak as arch(x), as shown in the plot above. Showing all your work and reasoning, you need to find appropriate a, b, c (keeping ten significant figures) with :

Solution 1

Solution 2

2. Showing all your work and reasoning, find the area of the triangle on the above plot given that: