Find the equation of a parabola with vertex(5,-3)and the axis of symmetry is parallel to the y-axis and pass through the point(9,5)

To find the equation of a parabola, we need to use the vertex form of the equation:

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

where (h, k) represents the vertex coordinates. In this case, the vertex is given as (5, -3), so we have:

y = a(x - 5)^2 - 3

Now, let's find the value of 'a'. Since the axis of symmetry is parallel to the y-axis, the equation will have the form x = c, where c is a constant. Since the point (9,5) lies on the axis of symmetry, we have x = 9. Therefore, we substitute x = 9 and y = 5 into the equation:

5 = a(9 - 5)^2 - 3

Now, we can solve for 'a':

5 = a(4)^2 - 3
5 = 16a - 3
16a = 8
a = 8/16
a = 1/2

Substituting this value of 'a' back into the equation, we have:

y = (1/2)(x - 5)^2 - 3

So, the equation of the parabola is y = (1/2)(x - 5)^2 - 3.