# How do you write y=x^2-4x+2 into vertex form?

Apr 30, 2015

The vertex form of a quadratic function is given by
$y = a {\left(x - h\right)}^{2} + k$, where $\left(h , k\right)$ is the vertex of the parabola.

We can use the process of Completing the Square to get this into the Vertex Form.

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

$\to y - 2 = {x}^{2} - 4 x$ (Transposed 2 to the Left Hand Side)

Now we ADD $4$ from each side to complete the square

$\to y - 2 + 4 = {x}^{2} - 4 x + {2}^{2}$

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

-> color(green)( y =1* (x-2)^2 - 2 is the Vertex Form

The vertex of the Parabola is$\left\{2 , - 2\right\}$