ANSWER
The resulting parabola in vertex form is:
[tex](x - 4) = 4( {y + 3)}^{2}[/tex]
EXPLANATION
The original equation of the parabola is given as
[tex]x = 4 {y}^{2} [/tex]
This parabola has its vertex at the origin.
If the graph of this parabola is shifted four units right and three units down, then the new equation is:
[tex](x - 4) = 4( {y + 3)}^{2}[/tex]
This the equation of the transformed parabola.
Its vertex is now at (4,-3).
