How deep is a parabola 4ft from edge. Word Problem.
A cross-section of an irrigation canal is a parabola. If the surface of the water is 33ft wide and the canal is 15ft deep at the center, how deep is it 4ft from the edge?
I assume the following is how it's done. Again, looking more towards confirmation and possible corrections if incorrect. Thanks.
Equation is y=ax^2
15 = a(16.5)^2
So, to get depth at 4 ft from edge, I assume my new x value is 12.5.
Derived from 16.5 - 4 = 12.5
y= 0.055 * (12.5)^2
y = 8.59
To get depth, I assume subtract from center depth of 15ft.
15ft - 8.59ft = 6.41ft
Answer is 6.41ft.