the squared variable is the "x", therefore is a vertical parabola so its axis of symmetry will come from the vertex's x-coordinate.
now, let's find the vertex of it.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
y=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{-8}x\stackrel{\stackrel{c}{\downarrow }}{-15}
\qquad \qquad
\left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)
\\\\\\
\left( -\cfrac{-8}{2(-2)}~~,~~\qquad \quad \right)\implies \left( -2~~,~~\qquad \right)
\\\\\\
\stackrel{\textit{axis of symmetry}}{x=-2}[/tex]
