THE SAINT LOUIS GATEWAY ARCH

The Saint Louis Gateway Arch (pictured at right) has a shape much like a parabola. Suppose the Gateway Arch can be approximated by image, where both x and y represent distances in feet and the origin is the point on the ground directly below the arch's apex (its highest point).

a. Find the x–intercepts of the Gateway Arch. What does this information tell you? Use a calculator to evaluate your answers.

b. How wide is the arch at its base?

c. How tall is the arch? How did you find your solution?

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3 Answers

A)
y=630-0.00635xx
x intercepts:
0=630-0.00635xx
-630=-0.00635xx
99212.5984251968=xx
sqrt(99212.5984251968)=
314.980314345511
and
-314.980314345511

X intercepts:
(-314.980314345511,0)
and
(+314.980314345511,0)

y intercept:
y=630-0.0065xx
y=630-0.0065*0
y=630
(0,630)

B)
Width
abs(x intercept)+abs(x intercept)
abs(+314.980314345511)+abs(-314.980314345511)=
629.960628691022 feet

C)
Height
630 feet (y intercept)
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