Answer:
the vertex is (3,-2), the focus is (3,-7/4), and the directrix is y=-9/4
Explanation:
in order to find the vertex, you convert the equation into vertex form so
y=(x-3)^2-2
With this, we can find the vertex which is at (3,-2)
In order to find the focus and diretrix, we need to find the value of p
We do this by creating the equation:
x^2=4py
in this case, (x-3)^2=4p(y+2) so 4p must equal 1 so p is 1/4
In order to find the focus, we add the value of p to the y coordinate of the vertex so the focus is (3,-2+1/4) which is (3,-7/4)
In order to find the directrix, we subtract the value of p to the y coordinate of the vertex so the directrix passes through the point (3,-2-1/4) which is (3,-9/4)
When we graph this parabola, we can tell that the directrix will be in the form of y = a and since this line passes through (3,-9/4) the directrix is y=-9/4
I hope you understand this explanation.