SOLUTION: A road is 32 feet wide is 0.4 foot higher in the center then it is on its sides. a) Find the equation of the parabola (Assume that the origin is at the center of the road) - Show

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A road is 32 feet wide is 0.4 foot higher in the center then it is on its sides. a) Find the equation of the parabola (Assume that the origin is at the center of the road) - Show       Log On


   

Question 390339: A road is 32 feet wide is 0.4 foot higher in the center then it is on its sides.
a) Find the equation of the parabola (Assume that the origin is at the center of the road) - Show all work
b) How far from the center of the road is the road surface 0.1 foot lower than in the middle? -show all work.
please show work and thank you.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A road is 32 feet wide is 0.4 foot higher in the center then it is on its sides.
a) Find the equation of the parabola (Assume that the origin is at the center of the road)
Using ax^2 + bx + c = y
Since the center is at origin, (x=0) then c = +.4
x=-16; y=0
-16^2a - 16b + .4 = 0
256a - 16b = -.4
x=16; y=0
16^2a + 16b + .4 = 0
256a + 16b = -.4
:
add these two equations
256a - 16b = -.4
256a + 16b = -.4
-------------------adding eliminates b
512a = -.8
a = %28-.8%29%2F512
a = -.0015625
:
Find b, it will equal 0, as you can see
-.0001562(256) + 16b = -.4
-.4 + 16b = -.4
16b = -.4 + .4
16b = 0
b = 0
Therefore:
The equation: -.0015625x^2 + .4 = y
:
:
b) How far from the center of the road is the road surface 0.1 foot lower than in the middle?
y = .3
-.0015625x^2 + .4 = .3
-.0015625x^2 = .3 - .4
-.0015625x^2 = -.1
x^2 = %28-.1%29%2F%28-.0015625%29
x^2 = 64
x = sqrt%2864%29
x = 8 ft from the center it is .1 ft lower than the middle