Step 1
Write the parabola in vertex form eqaution

where

Step 2
Find the required equation
The distance between the vertex and the focus = a
Therefore,

Hence with the formula for the distance between two points we have
![\begin{gathered} D=\sqrt[]{(0-0)^2+(-2-1)^2}^{}_{} \\ D=\sqrt[]{0^2+(-3)^2} \\ D=\sqrt[]{0+9} \\ D=\sqrt[]{9} \\ D=3 \\ a=D=3 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/sof9wpohq3yyl1zzyzwys4uhluv3lskwuf.png)
Step 3
Get the required equation by substitution

Hence in vertex form, the equation of the parabola will be

The answer is written as;
