Answer:
3 ft.
Step-by-step explanation:
We have that the parabola formula has the following general equation:
x ^ 2 = 4py
p would come being the distension of the vertex until the focus.
They tell us that this value is 3, that is to say p = 3. Replacing we have:
x ^ 2 = 4 * 3 * y
x ^ 2 = 12 * y
reorganizing for and, we are left with:
y = (1/12) * x ^ 2
We know that the opening is 12 feet wide, therefore, the parabola, being symmetry, must be distributed in the same way, in two equal parts, that is, 12/2 = 6. Therefore, being vertical on the x axis must take values of (-6, y), (6, y).
Which means that the value of x is 6 or -6. (it doesn't matter which of the two is when it is squared)
Replacing in the equation obtained:
y = (1/12) * (6 ^ 2)
y = 3
Therefore the depth is equal to 3 ft.
