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

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

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Answer 1 · 2018-06-24T08:52:03

${(x + 1)}^{2} - 1$ $(x+1)^2-1$

Explanation:

$f (x) = x^{2} + 2 x$ $f(x)=x^2+2x$
expanding this with $+ 1 - 1$ $+1-1$ gives:
$f (x) = x^{2} + 2 x + 1 - 1$ $f(x)=x^2+2x+1-1$ which is equivalent to $f (x) = x^{2} + 2 \cdot 1 \cdot x + 1^{2} - 1$ $f(x)=x^2+2*1*x+1^2-1$
Now we can apply the reverse of the binomial formula and get:
$f (x) = {(x + 1)}^{2} - 1$ $f(x)=(x+1)^2-1$

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

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