Answer:
The vertex would be (-1, -5).
Step-by-step explanation:
In order to find this, first find the x-coordinate of the vertex. You can do this by calculating out -b/2a in which a is the coefficient of x^2 and b is the coefficient of x.
-b/2a
-(-2)/2(-1)
2/-2
-1
So we know the x-coordinate to be -1. Now we plug that into the equation and find the y value.
-x^2 - 2x - 6
-(-1)^2 - 2(-1) - 6
-(1) + 2 - 6
-5
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{-2}{2(-1)}~~,~~-6-\cfrac{(-2)^2}{4(-1)} \right)\implies \left( \cfrac{2}{-2}~,~-6+\cfrac{4}{4} \right) \\\\\\ (-1~,~-6+1)\implies (-1~,~-5)[/tex]
