To solve this problem you must apply the proccedure shown below:
1. You have that the standard form of the equation of the parabola must satisfy the following conditions given in the exercise above:
Focus: (-1,4) and Directrix: y=2
2. Therefore you have:
√(x0-(-1))²+(y0-4)²=|y0-2|
(x0+1)²+(y0-4)²=(y0-2)²
3. When you simplify the expression above and clear y0, you obtain:
y0=y
y=1/4(x²+2x+13)
y=(x²/4)+(x/2)+(13/4)
Therefore, the answer is: y=(x²/4)+(x/2)+(13/4)