Answer: x=4
For any given equation of a parabola,
[tex](y-k)^2=4p(x-h)[/tex]
The directrix is found at x = h-p
From the given equation,
[tex](y-7)^2=-4(x-3)[/tex]
We know that 4p=-4. With this, we solve for p:
[tex]\begin{gathered} 4p=-4 \\ p=-\frac{4}{4} \\ p=-1 \end{gathered}[/tex]
The directrix would then be:
[tex]\begin{gathered} x=h-p \\ x=3-(-1) \\ x=3+1 \\ x=4 \end{gathered}[/tex]
