# How do you write f(x) = (x-3)^2 + 17 in standard form?

Jul 23, 2016

$y = {x}^{2} - 6 x + 26$

#### Explanation:

The given form is that of 'Vertex form' or 'Completing the Square'

We need to change this so that it is in the form of $y = a {x}^{2} + b x + c$

Write as $y = {\left(x - 3\right)}^{2} + 17$

This is the same as:

$y = \textcolor{b l u e}{\left(x - 3\right)} \textcolor{b r o w n}{\left(x - 3\right)} + 17$

Multiply out the brackets

$y = \textcolor{b r o w n}{\textcolor{b l u e}{x} \left(x - 3\right) \textcolor{b l u e}{- 3} \left(x - 3\right)} + 17$

$y = {x}^{2} - 3 x \text{ "-3x+9" } + 17$

$y = {x}^{2} - 6 x + 26$