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# Real Life Parabola: St. Louis Gateway Arch

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by

## Kyle Watson

on 5 July 2015

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#### Transcript of Real Life Parabola: St. Louis Gateway Arch

What It Is
St. Louis Gateway Arch, Monument
Its Name
St. Louis Arch
Where It is Located
St. Louis Missouri
It was supposed to provide 5,000 jobs but only provided less than 100.

Why I Chose It
Its one of the largest arches, and most famous.

Its History
The monument was finished on October 28, 1965. The monument was built to the vision of Thomas Jefferson and St. Louis’ role in westward expansion. It is made of stainless steel and is the world's tallest arch and the tallest monument in the western hemisphere. You can also go inside the monument.
Real Life Parabola: St. Louis Gateway Arch
Step by Step Explanation On How I Derived my Parabola
Step-by-Step Explanation on How I Derived my Quadratic Model:

1. First I determined the initial height of the St. Louis Gateway Arch, which is 0 feet.
2. I then determined the maximum height of the St. Louis Arch, 630 feet, and the length of the arch from the initial point to the maximum height, 315 feet. Thus, my vertex is (315, 630) with an initial height of 0.
3. I then wrote out the basic formula for vertex form parabolas since I know the vertex of the arch. y = a( x - h ) ^2 + k (h,k)->(315, 630)and then plugged my vertex and the ending point (630, 0) of my graph into the equation to find a. 0 = a(630-315) ^2 + 630
a = -0.00635
4. I then wrote out the basic formula to find a vertex of a parabola. x = -b/2a, I plugged in 315 for x and -0.00635 for a to find b for my standard form equation. b = 4.0005
5. We now have the equation : y = -0.00635x^2 + 4.0005x, where c = 0.
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