MATH help please?

Question

Highways surfaces are constucting with a roughly parabolic shape. This makes the centre of the raod higher than the sides so the water will drain off the road onto the shoulders.

In this problem the road is 7.6 m across. A cable is embedded in the road 156 cm from one side and the road is 9.4 cm thick at this point.

Find the equation of the parabola. find the MAXIMUM height of the road.

(the numbers in this problem may be very small, so your answers may be accurate to 7 decimal places)

If someone can please help me out it would be great, I must know all the necessary steps to completing this problem. Please show me all the steps!

Thanks,

Answer 1

Please see:
http://s210.photobucket.com/albums/bb64/oregfiu/?action=view¤t=parabola.jpg
Equation of the parabola is
y = k * x^2
(Coefficient k is to be find.)
Equation 1 (point A):
- a = k * 2240^2
Equation 2 (point B):
- a - 94 = k * 3800^2
From equations 1 and 2 find values of "a" and "k".
Maximum height of the road is - a + 94.
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Answer:
The equation of the parabola is y = - 0.00000997623 * y^2
The maximum height of the road is 144 mm.
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