Find the Vertex Form y=x^2+2x+1

$y = x^{2} + 2 x + 1$

Complete the square for $x^{2} + 2 x + 1$ .

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Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1, b = 2, c = 1$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{2}{2 (1)}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$d = \frac{2}{2 \cdot 1}$

Divide $1$ by $1$ .

$d = 1$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

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Simplify each term.

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Raise $2$ to the power of $2$ .

$e = 1 - \frac{4}{4 \cdot 1}$

Multiply $4$ by $1$ .

$e = 1 - \frac{4}{4}$

Divide $4$ by $4$ .

$e = 1 - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$e = 1 - 1$

Subtract $1$ from $1$ .

$e = 0$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $a {(x + d)}^{2} + e$ .

${(x + 1)}^{2} + 0$

Set $y$ equal to the new right side.

$y = {(x + 1)}^{2} + 0$

Find the Vertex Form y=x^2+2x+1

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