Parabola Word Problem

[ehmuhleewu]

The Saint Louis Gateway Arch has the shape of an inverted catenary, a curve that is roughly the shape of a parabola. From the ground level to the vertex, the Gateway Arch is 630 feet tall. At ground level the legs are 630 feet apart. The legs extend 60 feet below ground level to anchor into bedrock. Given this information, what is the equation of a parabola that approximates the shape of the Gateway Arch? Assume that the origin of the coordinate system is at ground level midway between the legs of the arch. Give the equation in standard form: y=ax^2+bx+c

Any help with this problem would be much appreciated! Please give detailed explanations, thanks!

 

[stapel]

The Saint Louis Gateway Arch has the shape of an inverted catenary, a curve that is roughly the shape of a parabola. From the ground level to the vertex, the Gateway Arch is 630 feet tall. At ground level the legs are 630 feet apart. The legs extend 60 feet below ground level to anchor into bedrock. Given this information, what is the equation of a parabola that approximates the shape of the Gateway Arch? Assume that the origin of the coordinate system is at ground level midway between the legs of the arch. Give the equation in standard form: y=ax^2+bx+c

Think about the parabola being centered on the y-axis, with "ground level" being the x-axis.

Then where is the vertex?

Where are the x-intercepts?

With these three points, what equation do you get? :wink:

 

[HallsofIvy]

Drawing a picture should help and clarify what stapel is saying.