St.+Louis+Arch

chapter 12 project will be about the St. Louis Arch. Baikleem Choi 최백림 S t. Louis Arch = = =

= = = = = = Mathematical description of the Gateway Arch. = = Both the height and the width of the arch is 630 feet.  The cross-sections of the arch's legs are equilateral triangles, narrowing from 54 feet per side at the bases to 17 feet per side at the top. Each wall consists of a stainless steel skin covering a sandwich of two carbon steel walls with reinforced concrete in the middle from ground level to 300 feet, with carbon steel to the peak. The arch is hollow to accommodate a unique tram system that takes visitors to an observation deck at the top. =

I graphed my parabola using EXCEL. I used the two bottom points and the top point. Then I added a trend line and added the equation and that is how I got my equation and graph.

**Historical Description**

 The gateway Arch reflects St. Louis' role in the Westward Expansion of the United States during the ninteenth century. the park is a memorial to Thomas Jefferson's role in opening the West to the pioneers who helped shape its history, and to Dred Scott who sued for his freedom in the Old Courthouse.

**Equations**

﻿Vertex Form: **y-630=-0.0063(x-315)^2 ** Standard Form: **y=-0.0063x^2+4x** Factor form:  **y=-0.0063x*(x-630)** The vertex of my parabola is (315,630) you can tell that by finding half of the width; in tis case the x-line which is 315. then you find the height of the parabola which is 630. This vertex is the maximum. the y-intercept is 0 and it represents the bottom left point.The x-intercepts are 0 and 630.

The discriminant is 16.0252. My parabola is not factorable over the integers because 16.0252 is not a perfect square. Since 16.0252 is a positive number, it means that there are two solutions to the equation. The two solutions are 0 and 630. The x-intercepts signify the two holding poles that are holding the Arch up. To find the x-intercepts you have to factor the parabola's equations then find the opposite of each constant in the parenthesis.


 * PROBLEM **

Find the two x-intercepts when the arch is half way up.

Answer X is about 120 and 500