# What is the vertex of y = x^2 − 4x + 3?

Oct 30, 2015

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

#### Explanation:

First, find the axis of symmetry of the equation using $x = \frac{- b}{2 a}$, where the values of $a$ and $b$ comes from $y = a {x}^{2} + b x + c$

In this case, $b = - 4$ and $a = 1$.

So the axis of symmetry is $x = \frac{- \left(- 4\right)}{\left(2\right) \left(1\right)}$
$x = 2$

Then substitute the $x$ value into the equation to find the $y$ co-ordinate.

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

So the co-ordinates of the vertex are $\left(2 , - 1\right)$