Write as an Equation f(x)=3(x+3)^2-2

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

Rewrite the function as an equation.

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

Simplify $3 {(x + 3)}^{2} - 2$ .

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $3$ by $3$ .

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

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

Add $3 x$ and $3 x$ .

$y = 3 (x^{2} + 6 x + 9) - 2$

$y = 3 (x^{2} + 6 x + 9) - 2$

Apply the distributive property.

$y = 3 x^{2} + 3 (6 x) + 3 \cdot 9 - 2$

Simplify.

Multiply $6$ by $3$ .

$y = 3 x^{2} + 18 x + 3 \cdot 9 - 2$

Multiply $3$ by $9$ .

$y = 3 x^{2} + 18 x + 27 - 2$

$y = 3 x^{2} + 18 x + 27 - 2$

$y = 3 x^{2} + 18 x + 27 - 2$

Subtract $2$ from $27$ .

$y = 3 x^{2} + 18 x + 25$

$y = 3 x^{2} + 18 x + 25$

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