# How do I use the vertex formula to determine the vertex of the graph for f(x)= -x^2-6x?

May 8, 2015

You know the graph of that function is a parabola with vertical axis of symmetry, because it's:

$y = a {x}^{2} + b x + c$, with $a = - 1 , b = - 6 \mathmr{and} c = 0$,

so you can use the vertex formula

${x}_{v} = - \frac{b}{2} a = - \frac{- 6}{- 2} = - 3$
${y}_{v} = f \left({x}_{v}\right) = - {\left(- 3\right)}^{2} - 6 \cdot \left(- 3\right) = - 9 + 18 = 9$

so $v = \left(- 3 , 9\right)$