Thread: 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

y=15
x= 16.5

15 = a(16.5)^2
a= 0.055

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

So:

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.

Correct? Thanks.

Method looks good to me, though I didn't check the mutliplication, subtraction, etc.

Good enough for me. I've checked the calculations several times. Same answer. Was debating with someone who said the depth would be the 8.59ft. But, I was 98% positive it would be 6.41ft since the 8.59 is the distance from the BOTTOM of the canal to the point at 8.59ft, not the distance from the surface of the water DOWN to the point, which is really what depth is. You saying method is good confirms I was correct. Thank you.

Yep, you are right. 8.59 is the y value, which represents the height of your function, or more specifically, the height of the bottom of the canal, and not the water height. Cool problem.