SOLUTION: An arch is in the shape of a parabola. It has a span of 348 feet and a maximum height of 29 feet. Find the equation of the parabola. Determine the distance from the center at whi

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: An arch is in the shape of a parabola. It has a span of 348 feet and a maximum height of 29 feet. Find the equation of the parabola. Determine the distance from the center at whi      Log On


   

Question 1198215: An arch is in the shape of a parabola. It has a span of 348 feet and a maximum height of 29 feet.
Find the equation of the parabola.
Determine the distance from the center at which the height is 11 feet.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the parabola is open downward and its origin is at the point (+0,+0),
vertex is at (+0,+29)
the +x-intercepts are +348%2F2=174 feet away from the origin at (+-174,+0) (+174,+0)

use three points above

+y+=+ax%5E2+%2Bbx%2Bc
since vertex at (0,29)
29+=+a%2A0%5E2+%2Bb%2A0%2Bc
c=29

so far your equation is
y+=+ax%5E2+%2Bbx%2B29

use (-174,0)

0=+a%28-174%29+%5E2+%2Bb%28-174%29+%2B29
0=30276a+-174b+%2B29
a=%28174b+-29%29%2F30276..........eq1

use (174,0)
0=+a%28174%29+%5E2+%2Bb%28-174%29+%2B29
0=30276a+%2B174b+%2B29
a=%28-174b+-29%29%2F30276..........eq2

then

%28174b+-29%29%2F30276=%28-174b+-29%29%2F30276
174b+-29=-174b+-29
348+b+=+0
b+=+0

go to

a=%28174%2A0+-29%29%2F30276..........eq1 plug in b+=+0
a=+-29%2F30276
a=+-1%2F1044


your equation is:

y+=+-%281%2F1044%29x%5E2+%2B29



then find x when y=11
11+=+-%281%2F1044%29x%5E2+%2B29
x%5E2+=+18792
x+=+sqrt%2818792%29
x+=+137.1ft

the distance from the center at which the height is 11 feet is +137.1ft