SOLUTION: The shape of the gateway arch in st. Louis, Missouri, is a catenary curve, which closely resemble a parabola. The function {{{ y = -2x^2/315 + 4x }}} models the shape of the arch,

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Question 518758: The shape of the gateway arch in st. Louis, Missouri, is a catenary curve, which closely resemble a parabola. The function models the shape of the arch, where y is the height in feet and x is the horizontal distance from the base of the left side of the arch in feet.
a)Find the vertex
b) Describe a reasonable domain and range for the function. Explain.
c) According to the model, what is the maximum height of the arch
d) What is the width of the arch at the base?
Answer by ankor@dixie-net.com(22740) (Show Source):
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The shape of the gateway arch in st. Louis, Missouri, is a catenary curve, which closely resemble a parabola. The function models the shape of the arch, where y is the height in feet and x is the horizontal distance from the base of the left side of the arch in feet.
:
Convert the coefficient of x^2 to a decimal = -.00635
:
a)Find the vertex
Find the axis of symmetry
x =
x = 315 ft, from the left side of the base
Find y (the height)

y = -630 + 1260
y = 630 ft high
vertex, 315, 630
:
b) Describe a reasonable domain and range for the function. Explain.
domain 0 to 630; range 0 to 630 (only positive values here)
:
c) According to the model, what is the maximum height of the arch
630 ft
d) What is the width of the arch at the base?
2(315) = 630 ft
:
A graph of this equation illustrates this well