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

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

Step 1

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

$f (x) = a x^{2} + b x + c$

Step 2

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$f (x) = - 3 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1) - 3$

Multiply $x$ by $1$ .

$f (x) = - 3 (x^{2} + x + 1 x + 1 \cdot 1) - 3$

Multiply $x$ by $1$ .

$f (x) = - 3 (x^{2} + x + x + 1 \cdot 1) - 3$

Multiply $1$ by $1$ .

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

Add $x$ and $x$ .

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

Apply the distributive property.

$f (x) = - 3 x^{2} - 3 (2 x) - 3 \cdot 1 - 3$

Simplify.

Multiply $2$ by $- 3$ .

$f (x) = - 3 x^{2} - 6 x - 3 \cdot 1 - 3$

Multiply $- 3$ by $1$ .

$f (x) = - 3 x^{2} - 6 x - 3 - 3$

Step 3

Subtract $3$ from $- 3$ .

$f (x) = - 3 x^{2} - 6 x - 6$