Given equation:
The general expression for a parabola equation in vertex form:
[tex]y^2\text{ =4ax}[/tex]
Where the axis of the parabola is the x-axis and the origin is zero
Writing the equation in vertex form takes the following steps:
1. Re-arrange the equation:
[tex]\begin{gathered} y^2-x-4y+3\text{ = 0} \\ y^2-4y\text{ - x + 3 = 0} \end{gathered}[/tex]
Factoring out:
[tex](y-2)^2-4\text{ -x + 3 = 0}[/tex]
Re-arranging further:
[tex](y-2)^2\text{ = (x+1)}[/tex]
Hence, the equation of the parabola is Option C
