# What is the axis of symmetry and vertex for the graph f(x)=x^2-2x-6?

Jun 2, 2017

$\text{axis of symmetry} \implies x = 1$

$\text{vertex} \implies \left(1 , - 7\right)$

#### Explanation:

For a parabola $f \left(x\right) = a {x}^{2} + b x + c$, the axis of symmetry is given by: x = -b/(2a.

Also, the vertex is given by $\left(\frac{- b}{2 a} , f \left(\frac{- b}{2 a}\right)\right)$ since it lies on the axis of symmetry.

Therefore, our axis of symmetry for this graph is given by:

$x = - \frac{b}{2 a} = - \frac{- 2}{2 \left(1\right)} = 1$

And the vertex is therefore given by $\left(1 , f \left(1\right)\right)$.

$f \left(1\right) = {1}^{2} - 2 \left(1\right) - 6$

$f \left(1\right) = 1 - 2 - 6 = - 7$

So the vertex is $\left(1 , - 7\right)$