orWatch a videoWrite the equation in vertex form for the parabola with focus (0,9) and directrix y=–3.Simplify any fractions.

The vertex form of a parabola is given by the equation y = a(x-h)² + k, where (h,k) is the vertex of the parabola.

The vertex of a parabola is the midpoint between the focus and the directrix. Given the focus (0,9) and the directrix y=-3, we can find the vertex as follows:

The x-coordinate of the vertex is the same as the x-coordinate of the focus, which is 0.

The y-coordinate of the vertex is the average of the y-coordinate of the focus and the y-coordinate of the directrix, which is (9 - 3) / 2 = 6.

So, the vertex of the parabola is (0,6).

The value of 'a' in the vertex form of a parabola is given by 1/(4f), where f is the distance from the vertex to the focus or to the directrix. In this case, f = 9 - 6 = 3, so a = 1/(4*3) = 1/12.

Therefore, the equation of the parabola in vertex form is y = 1/12 * x² + 6.