Write in Standard Form y=2(x+4)^2-21

$y = 2 {(x + 4)}^{2} - 21$

Step 1

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

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

Step 2

Simplify each term.

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

$y = 2 ((x + 4) (x + 4)) - 21$

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

Apply the distributive property.

$y = 2 (x (x + 4) + 4 (x + 4)) - 21$

Apply the distributive property.

$y = 2 (x \cdot x + x \cdot 4 + 4 (x + 4)) - 21$

Apply the distributive property.

$y = 2 (x \cdot x + x \cdot 4 + 4 x + 4 \cdot 4) - 21$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = 2 (x^{2} + x \cdot 4 + 4 x + 4 \cdot 4) - 21$

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

$y = 2 (x^{2} + 4 \cdot x + 4 x + 4 \cdot 4) - 21$

Multiply $4$ by $4$ .

$y = 2 (x^{2} + 4 x + 4 x + 16) - 21$

Add $4 x$ and $4 x$ .

$y = 2 (x^{2} + 8 x + 16) - 21$

Apply the distributive property.

$y = 2 x^{2} + 2 (8 x) + 2 \cdot 16 - 21$

Simplify.

Multiply $8$ by $2$ .

$y = 2 x^{2} + 16 x + 2 \cdot 16 - 21$

Multiply $2$ by $16$ .

$y = 2 x^{2} + 16 x + 32 - 21$

Step 3

Subtract $21$ from $32$ .

$y = 2 x^{2} + 16 x + 11$

Step 4