# How do you write the Vertex form equation of the parabola f(x) = x^2 - 6x + 5?

Feb 20, 2016

$y = {\left(x - 3\right)}^{2} - 4$

#### Explanation:

The standard form of a quadratic function is y = $a {x}^{2} + b x + c$

the function here $y = {x}^{2} - 6 x + 5 \text{ is in this form}$

and by comparison : a = 1 , b = - 6 and c = 5

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

x-coord of vertex $= \frac{- b}{2 a} = - \frac{- 6}{2} = 3$

and y-coord = ${\left(3\right)}^{2} - 6 \left(3\right) + 5 = 9 - 18 + 5 = - 4$

hence a = 1 , (h , k ) = (3 , -4 )

$\Rightarrow y = {\left(x - 3\right)}^{2} - 4 \text{ is equation in vertex form }$