1. Write out the correct arch function and simplify, keeping ten significant figures:

___________________

2. Next, find a quadratic function f(x) that has the same x-intercepts, and the same y-intercept as arch(x), and create a very accurate hand drawn graph on the plot above. You need to find appropriate a, b, c with:

3. Prove that the height of the arch from the ground to the highest point on the top of the structure is 630 ft. Make sure to draw an accurate diagram and to provide a complete logical argument. Note that (a) the function arch(x) goes through the centroid of the arch structure (the equilateral triangles), (b) the centroid of a triangle is the point of intersection of all the medians of the triangle, (c) the centroid is located along each median 2/3 of the way from the vertex to the midpoint of the opposite side.
 
 
 
 
 

4. Prove that the base of the arch at ground level from the leftmost outside point on the structure to the rightmost outside point on the structure is 630 ft. Make sure to draw an accurate diagram and to provide a complete logical argument.