i need help finding the width of the arch at the base?

Question

The shape of the Gateway Arch in St. Louis, Missouri, is a catenary curve, which closely resembles a parabola. The following function: y= -2/315 x^2 + 4x models the shape of the arch in feet.


i need help finding the width of the arch at the base.. can u please show me how you did it so i learn. thanks so0o much

Answer 1

y = -2/315 x² + 4x

Imagine graphing this equation, where the x-axis is the earth and the curve begins at the origin (0,0).

Then the width of the arch at the base will be the x-value where it crosses the x-axis for the second time, right?

So you need to set the equation equal to zero and solve.

0 = -2/315 x² + 4x

0 = x(-2/315 x + 4)

x = 0 or

-2/315 x + 4 = 0

-2/315x = -4

x = 630 feet wide

Answer 2

I expect the idea is that ground level is y = 0,
and so you have to solve
-2/315 x^2 + 4x = 0
I'll do it below, but if you know how to do it yourself, do so and don't check mine till you've finished.








































































































x((-2/315)x + 4) = 0
x = 0 or 2x/315 = 4
x = 0 or 630
Thus the width of the arch at the base is 630 feet.