SOLUTION: The Gateway Arch in a city has the shape of a catenary (a U-shaped curve similar to a parabola). It can be approximated by the following model, where x and y are measured in feet.

Algebra ->  Graphs -> SOLUTION: The Gateway Arch in a city has the shape of a catenary (a U-shaped curve similar to a parabola). It can be approximated by the following model, where x and y are measured in feet.       Log On


   

Question 1139603: The Gateway Arch in a city has the shape of a catenary (a U-shaped curve similar to a parabola). It can be approximated by the following model, where x and y are measured in feet.
y = -(3/1000)(x + 400)(x - 400). How high is the arch?
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+-.003%2A%28+x%5E2+-+160000+%29+
+y+=+-.003x%5E2+%2B+480+
This is a parabola with a maximum. The vertex
( max ) has:
+x%5Bmax%5D+=+-b%2F%282a%29+
+x%5Bmax%5D+=+0%2F%28-.006%29+
+x%5Bmax%5D+=+0+
and
+y%5Bmax%5D+=+-.003%2A0%5E2+%2B+480+
+y%5Bmax%5D+=+480+
The arch is 480 ft high