SOLUTION: The Gateway Arch in St. Louis, Missouri, has a shape similar to that of a parabola. The edge of the arch can be modeled by h= -(2/319)x^2+(92/21)x-(864/7) where x and h are measu

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Question 242592: The Gateway Arch in St. Louis, Missouri, has a shape similar to that of a parabola. The edge of the arch can be modeled by
h= -(2/319)x^2+(92/21)x-(864/7)
where x and h are measured in feet. How high is the arch? Answer in units of ft.
Thanks!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The Gateway Arch in St. Louis, Missouri, has a shape similar to that of a parabola.
The edge of the arch can be modeled by
h= -(2/319)x^2+(92/21)x-(864/7)
where x and h are measured in feet. How high is the arch? Answer in units of ft.
:
The graph of this equation:

:
The axis of symmetry would be thru the highest point:
The equation for this: x = -b/(2*a)
:
In this equation: a=-2/319, b=92/21
:
x = %28-92%2F21%29%2F%282%2A%28-2%2F319%29%29 = %2892%2F21%29%2F%284%2F319%29 = %2892%2F21%29%2A%28319%2F4%29 = 29349%2F84 = 349.38 ft is the axis of symmetry
:
How high?
Substitute 349.38 for x in the given equation to find the height
:
h= -(2/319)x^2 + (92/21)x - (864/7)
h = -(2/319)(349.38^2) + (92/21)(349.38) - (864/7)
I'll let you do the math here