# What is the axis of symmetry and vertex for the graph y = x ^2 - 4 x + 3?

May 26, 2017

Vertex $\left(2 , - 1\right)$
Axis of symmetry $x = 2$

#### Explanation:

Given -

$y = {x}^{2} - 4 x + 3$

Vertex -
x-coordinate of the vertex

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

y-coordinate of the vertex

$y = {2}^{2} - 4 \left(2\right) + 3 = 4 - 8 + 3 = - 1$

Vertex $\left(2 , - 1\right)$

Axis of symmetry $x = 2$

May 26, 2017

$X = 2$

$\left(2 , - 1\right)$

#### Explanation:

Another way of finding the axis and vertex is to complete the square

$y = {x}^{2} - 4 x + 3$

$y = {\left(x - 2\right)}^{2} - 1$

for the vertex find the $x \text{ }$ value that makes the bracket $= 0$

$x = 2 \implies y = - 1$

vertex $\left(2 , - 1\right)$

axis of symmetry simply the the x-value above $X = 2$

with the graph as before