Write in Standard Form y=2(x+3)^2-5

$y = 2 {(x + 3)}^{2} - 5$

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 ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$y = 2 ((x + 3) (x + 3)) - 5$

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$y = 2 (x (x + 3) + 3 (x + 3)) - 5$

Apply the distributive property.

$y = 2 (x \cdot x + x \cdot 3 + 3 (x + 3)) - 5$

Apply the distributive property.

$y = 2 (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) - 5$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = 2 (x^{2} + x \cdot 3 + 3 x + 3 \cdot 3) - 5$

Move $3$ to the left of $x$ .

$y = 2 (x^{2} + 3 \cdot x + 3 x + 3 \cdot 3) - 5$

Multiply $3$ by $3$ .

$y = 2 (x^{2} + 3 x + 3 x + 9) - 5$

Add $3 x$ and $3 x$ .

$y = 2 (x^{2} + 6 x + 9) - 5$

Apply the distributive property.

$y = 2 x^{2} + 2 (6 x) + 2 \cdot 9 - 5$

Simplify.

Multiply $6$ by $2$ .

$y = 2 x^{2} + 12 x + 2 \cdot 9 - 5$

Multiply $2$ by $9$ .

$y = 2 x^{2} + 12 x + 18 - 5$

Step 3

Subtract $5$ from $18$ .

$y = 2 x^{2} + 12 x + 13$

Step 4