Write in Standard Form y=(x+4)^2-1

$y = {(x + 4)}^{2} - 1$

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 ${(x + 4)}^{2}$ as $(x + 4) (x + 4)$ .

$y = (x + 4) (x + 4) - 1$

Expand $(x + 4) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$y = x (x + 4) + 4 (x + 4) - 1$

Apply the distributive property.

$y = x \cdot x + x \cdot 4 + 4 (x + 4) - 1$

Apply the distributive property.

$y = x \cdot x + x \cdot 4 + 4 x + 4 \cdot 4 - 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot 4 + 4 x + 4 \cdot 4 - 1$

Move $4$ to the left of $x$ .

$y = x^{2} + 4 \cdot x + 4 x + 4 \cdot 4 - 1$

Multiply $4$ by $4$ .

$y = x^{2} + 4 x + 4 x + 16 - 1$

Add $4 x$ and $4 x$ .

$y = x^{2} + 8 x + 16 - 1$

Subtract $1$ from $16$ .

$y = x^{2} + 8 x + 15$