St. Louis Gateway Arch

Parabola Project

Halle G.


My parabola: St. Louis arch (Gateway arch)

The Finnish-American architect Eero Saarinen and structural engineer Hannskarl Bandel designed the St. Louis Arch in 1947. The arch is 630 feet wide at its base and is 630 feet tall, which makes it the tallest monument in the US. The span of its legs is 630 feet. Construction of the arch started on February 12th, 1963, ended on October 28th, 1965, and it was opened to the public on July 10th, 1967. Eero Saarinen died of a brain tumor before the arch was finished at the age of 51.
The vertex of the parabola is (315,630), and the y-intercept is (0,0). I can find the y-intercept without looking at the graph by looking at my coordinates for the y-intercept. I can find the vertex without looking at the graph, because I know that the vertex form of my graph is y-630=-.0063(x-315)^2, with (315,630) being the vertex. The vertex is a maximum, because the vertex is at the highest point. The height of the parabola is (315,630). The X-intercepts are (630, 0) and (0,0).
My parabola has two x-intercepts, and they are (630,0) and (0,0). You could find them without looking at the graph by knowing that it starts at (0,0), and then measuring the width of the parabola. The parabola opens down, so a is negative. The equation is -0.0063x^2+4x+0.

arch.png
This parabola opens down, so that makes a negative.

4.
a. Y-630=-.0063(x-315)^2—The formula for a vertex form equation is y-k=a(x-h)^2, where (h,k) is the vertex
b. Y=-.0063x^2+4x—This is the standard form of the equation; a does not equal 0 and the point (0,c) is the y-intercept
c. Y=-.0063(x-630)(x)—Factored form; the formula is y=a (x-r1)(x-r2), where r1 and r2 are the x-intercepts.
5. I used the quadratic formula to solve this problem. Y=75 when X=0 or when X=-.0252.

Work: -4± (insert radical sign here)4^2-4(.0063)(0)
2(.0063)

So, since the square root of 4^2-4(.0063) (0) is 4, I did -4 ± 4
2(.0063)

So, -4+4 is 0, and divided by 2 is 0, so that’s one of the solutions.

The other solution is -4-4 which is -8. Divide that by 2 (.0063), and you’ll get -.0252 as your other solution.

Therefore, X=0 and X=-.0252.