SOLUTION: A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 196 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 196 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.       Log On


   

Question 758377: A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 196 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A bridge is built in the shape of a parabolic arch.
The bridge arch has a span of 196 feet and a maximum height of 30 feet.
Find the height of the arch at 15 feet from its center.
:
Let the left side of the arch be at origin (0,0) then axis of symmetry
and max will be at x=98, y=30 and the right side: x=196,y=0
Using the form ax^2 + bx + c = y; c=0 so we can ignore that
x=98, y= 30
98^2a + 98b = 30
9604a + 98b = 30
and
x=196, y=0
196^2a + 196b = 0
38416a + 196b = 0
:
Multiply the 1st equation by 2, subtract from the above equation
38416a + 196b = 0
19208a + 196b = 60
-------------------subtraction eliminate b, find a
19208a = -60
a = -60/19208
a = -.0031237
:
Find b using the 1st equation
9604(-.0031237) + 98b = 30
-30 + 98b = 30
98b = 30 + 30
98b = 60
b = 60/98
b = .612
:
The equation for the arch: y = -.0031237x^2 + .612x
:
Graphically
+graph%28+300%2C+200%2C+-50%2C+220%2C+-10%2C+40%2C+-.0031237x%5E2%2B.612x%2C+29.27%29+
:
Find the height of the arch at 15 feet from its center. (Green line)
You can do this replace x with 83 and find y (height)
Do the same with x = 113