# What is the axis of symmetry and vertex for the graph f(x)= -x^2+4x-1?

May 1, 2016

The axis of symmetry is the line $x = 2$ and the vertex is $\left(2.3\right)$

#### Explanation:

The formula to find the axis of symmetry is: $x = \frac{- b}{2 a}$
$x = \frac{- 4}{2 \left(- 1\right)} = 2$

The vertex is on the axis of symmetry.
Substitute $x = 2$ into the equation to find the $y - v a l u e$
$y = - {\left(2\right)}^{2} + 4 \left(2\right) - 1$ which gives $y = 3$

Vertex is (2,3)