Answer:
[tex](x+3)^2=4(y-3)[/tex]
Step-by-step explanation:
Parabolas
In conic sections, the standard form of a parabola with a vertex at (h, k) is
[tex](x-h)^2=4p(y-k)[/tex] ,
when the parabola is parallel to the y-axis (opens up/down);
[tex](y-k)^2=4p(x-h)[/tex],
when the parabola is parallel to the x-axis (opens left/right);
The distance between the vertex and the directrix (line) is the same as the distance between the vertex and the focus point, this distance is represented by "p".
[tex]\hrulefill[/tex]
Solving the Problem
Determine Which Standard Form to Use
The parabola opens downwards, so we use [tex](x-h)^2=4p(y-k)[/tex].
Identifying the Parabola's Equation
The parabola has a vertex at (-3, 3), so h = -3 and k = 3.
The distance between the vertex and focus point (-3, 2) is 1, so p = 1.
Putting it all together,
[tex](x-(-3))^2=4(1)(y-3)[/tex]
[tex](x+3)^2=4(y-3)[/tex].
