Write as an Equation f(x)=-2(x+3)^2+14

$f (x) = - 2 {(x + 3)}^{2} + 14$

Step 1

Rewrite the function as an equation.

$y = - 2 {(x + 3)}^{2} + 14$

Step 2

Simplify $- 2 {(x + 3)}^{2} + 14$ .

Simplify each term.

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

$y = - 2 ((x + 3) (x + 3)) + 14$

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

Apply the distributive property.

$y = - 2 (x (x + 3) + 3 (x + 3)) + 14$

Apply the distributive property.

$y = - 2 (x \cdot x + x \cdot 3 + 3 (x + 3)) + 14$

Apply the distributive property.

$y = - 2 (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) + 14$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = - 2 (x^{2} + x \cdot 3 + 3 x + 3 \cdot 3) + 14$

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

$y = - 2 (x^{2} + 3 \cdot x + 3 x + 3 \cdot 3) + 14$

Multiply $3$ by $3$ .

$y = - 2 (x^{2} + 3 x + 3 x + 9) + 14$

Add $3 x$ and $3 x$ .

$y = - 2 (x^{2} + 6 x + 9) + 14$

Apply the distributive property.

$y = - 2 x^{2} - 2 (6 x) - 2 \cdot 9 + 14$

Simplify.

Multiply $6$ by $- 2$ .

$y = - 2 x^{2} - 12 x - 2 \cdot 9 + 14$

Multiply $- 2$ by $9$ .

$y = - 2 x^{2} - 12 x - 18 + 14$

Add $- 18$ and $14$ .

$y = - 2 x^{2} - 12 x - 4$