write the equation in vertex form, of a parabola with vertex (5, -1) and that passes through the point (6, 8)

Y = a(x-h)^2 + k.

8 = a(6-5)^2 - 1,
8 = a - 1, a = 9.

Y = 9(x-5)^2 - 1.

To write the equation of a parabola in vertex form, we can use the formula:

\(y = a(x - h)^2 + k\)

where (h, k) represents the vertex of the parabola.

Given that the vertex is (5, -1), we can substitute these values into the formula:

\(y = a(x - 5)^2 - 1\)

Now, we need to find the value of 'a' in order to complete the equation. To do this, we can use the fact that the parabola passes through the point (6, 8).

Substituting the coordinates of the given point (6, 8) into the equation, we have:

\(8 = a(6 - 5)^2 - 1\)

Simplifying further:

\(8 = a(1)^2 - 1 = a - 1\)

Now, solving for 'a':

\(a - 1 = 8\)
\(a = 8 + 1\)
\(a = 9\)

Therefore, the equation of the parabola, in vertex form, is:

\(y = 9(x - 5)^2 - 1\)