Parabola help!

Q1

Since the focus is to the right of the vertex, this parabola opens to the right

The form is

4a ( x - h)  = (y - k)^2

Where (h, k)    is the vertex  = (-5,2)    and "a"  is the distance from the vertex to the focus  = 4

So we have

4(4)(x + 5))  = (y - 2)^2        which we can write as

(y - 2)^2  = 16 ( x + 5)

Here's the graph : https://www.desmos.com/calculator/3ko051gwv7

Q2

Rearrange as...

2x^2 - 12x  = 3y - 12      complete the square on  x

2 (x^2 - 6x + 9)  = 3y - 12 + 18

2 ( x - 3)^2  =  3y + 6        divide through by 2

2(x - 3)^2  = 3(y + 2)       divide through by 2           

(x - 3)^2  = (3/2)( y + 2)

Here's the graph :   https://www.desmos.com/calculator/bbqwqfbnc2