this is a quadratic equation with a squared "x" variable, and therefore a vertical parabolic graph, and thus, the axis of symmetry will be from the vertex's x-coordinate, hmmmm what is its vertex coordiinate anyway?
[tex]\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
f(x)=\stackrel{\stackrel{a}{\downarrow }}{-3}x^2\stackrel{\stackrel{b}{\downarrow }}{+18}x\stackrel{\stackrel{c}{\downarrow }}{-7}
\qquad \qquad
\left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)
\\\\\\
\left( -\cfrac{18}{2(-3)}~~,~~\qquad \right)\implies \left( +\cfrac{18}{6}~~,~~\qquad \right)\implies (3~,\quad )
\\\\\\
\stackrel{\textit{axis of symmetry}}{x=3}[/tex]
