# How do you find the vertex and axis of symmetry, and then graph the parabola given by:  f(x)= -x^2+4x-1?

Sep 29, 2015

Vertex $\left(2 , 3\right)$
Axis of Symmetry $x = 2$

#### Explanation:

$f \left(x\right) = - {x}^{2} + 4 x - 1$

a=-1;b=4;c=-1

$x = \frac{- b}{2 a} = \frac{- 4}{2 \times \left(- 1\right)} = 2$

At x=2; f(x) =-(2)^2+4(2)-1
$f \left(x\right) = - 4 + 8 - 1 = 3$

Vertex $\left(2 , 3\right)$
Axis of Symmetry $x = 2$

Take a few points less than 2 and a few values greater than 2

x: y
-1: -6
0: -1
1: 2
2: 3
3: 2
4: -1
5: -6

graph{-x^2+4x-1 [-10, 10, -5, 5]}