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

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Answer 1 · 2016-07-23T10:48:37

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

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 $y=ax^2+bx+c$

Write as $y=(x-3)^2+17$

This is the same as:

$y=color(blue)((x-3)) color(brown)((x-3))+17$

Multiply out the brackets

$y=color(brown)(color(blue)(x)(x-3)color(blue)(-3)(x-3))+17$

$y=x^2-3x" "-3x+9" "+17$

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

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