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

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Answer 1 · 2017-10-12T18:24:20

$f(x)=(x+1)^2+2$

You can complete the square:

Subtract 3 on both sides:

$f(x)-3=x^2+2x$

Add 1 on both sides to make the right side a perfect square:

$f(x)-3+1=x^2+2x+1$

Combine like terms and factor:

$f(x)-2=(x+1)(x+1)$

Add 2 on both sides:

$f(x)=(x+1)^2+2$

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