Write in Standard Form y=(x+1)^2-3

$y = {(x + 1)}^{2} - 3$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Simplify each term.

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$y = (x + 1) (x + 1) - 3$

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$y = x (x + 1) + 1 (x + 1) - 3$

Apply the distributive property.

$y = x \cdot x + x \cdot 1 + 1 (x + 1) - 3$

Apply the distributive property.

$y = x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1 - 3$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot 1 + 1 x + 1 \cdot 1 - 3$

Multiply $x$ by $1$ .

$y = x^{2} + x + 1 x + 1 \cdot 1 - 3$

Multiply $x$ by $1$ .

$y = x^{2} + x + x + 1 \cdot 1 - 3$

Multiply $1$ by $1$ .

$y = x^{2} + x + x + 1 - 3$

Add $x$ and $x$ .

$y = x^{2} + 2 x + 1 - 3$

Subtract $3$ from $1$ .

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