Final answer:
The vertex form equation of the parabola is y = (25/8)(x - 9)^2 - 3.
Step-by-step explanation:
To write the vertex form equation of a parabola, we need to use the formula y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the vertex is (9, -3), so we have y = a(x - 9)^2 - 3.
Next, we need to find the value of a. The value of a can be determined from the distance between the vertex and the focus. In this case, the distance is 25/8. Since the parabola opens upwards, the value of a is positive, so the equation becomes y = a(x - 9)^2 - 3 = (25/8)(x - 9)^2 - 3.
Therefore, the vertex form equation of the parabola is y = (25/8)(x - 9)^2 - 3.