The vertex form of a parabolic equation is given by:
\[y = a(x - h)^2 + k\]
Where:
- (h, k) is the vertex of the parabola.
Given the vertex (6, -6), we have h = 6 and k = -6.
We also have a point that the parabola passes through, (8, -14).
Substitute these values into the equation:
\[-14 = a(8 - 6)^2 - 6\]
Simplify the equation:
\[-14 = 4a - 6\]
Now, isolate 'a':
\[4a = -14 + 6\]
\[4a = -8\]
\[a = -2\]
So, the value of 'a' is -2.
Now, we can write the equation of the parabola in vertex form:
\[y = -2(x - 6)^2 - 6\]
Therefore, the equation of the parabola in vertex form is \(y = -2(x - 6)^2 - 6\).