A parabola is expressed by a quadratic equation that is either facing on the right, left, upward or downward. Since the function given is opening to the left, then the standard form of the parabola equation is (y-k)^2 = -4a ( x-h) where (h,k) represents the coordinates of the vertex and a is the length of the latus rectum. The vertex is at (2,-4). Substituting, (y+4)^2 = -4a (x-2)
We can find a by substituting the other coordinate, (-3,-3). This is equal to
(-3+4)^2 = -4a (-3-2)
1 = -4a (-5)
4a = 1/5
Hence the formula becomes (y+4)^2 = -1/5 (x-2)
The coefficient of the squared term hence is 5 as we multiply the whole equation by 5 to convert to standard form.
