as you may know, the axis of symmetry will be a coordinate off the vertex of the equation, so...
[tex]\bf y-4x=7-x^2\implies y=7-x^2+4x\implies y=-x^2+4x+7
\\\\\\
\textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{llll}
y = &{{ 1}}x^2&{{ +4}}x&{{ +7}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)
\\\\\\
\left(-\cfrac{4}{2(-1)}~~,~~7-\cfrac{4^2}{2(-1)} \right)\quad thus\implies \stackrel{\textit{axis of symmetry}}{x=~~~~-\cfrac{4}{2(-1)}}[/tex]
