Question

Find the axis of symmetry y= -2x^2 -8x -15

Answer 1

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.


`\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}`