Trigonometry Examples

$f (x) = - 2 {(x - 2)}^{2} - 4$

Step 1

Factor $2$ out of $- 2 {(x - 2)}^{2} - 4$ .

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Step 1.1

Factor $2$ out of $- 2 {(x - 2)}^{2}$ .

$f (x) = 2 (- {(x - 2)}^{2}) - 4$

Step 1.2

Factor $2$ out of $- 4$ .

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

Step 1.3

Factor $2$ out of $2 (- {(x - 2)}^{2}) + 2 (- 2)$ .

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

Step 2

Rewrite ${(x - 2)}^{2}$ as $(x - 2) (x - 2)$ .

$f (x) = 2 (- ((x - 2) (x - 2)) - 2)$

Step 3

Expand $(x - 2) (x - 2)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$f (x) = 2 (- (x (x - 2) - 2 (x - 2)) - 2)$

Step 3.2

Apply the distributive property.

$f (x) = 2 (- (x \cdot x + x \cdot - 2 - 2 (x - 2)) - 2)$

Step 3.3

Apply the distributive property.

$f (x) = 2 (- (x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2) - 2)$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $x$ by $x$ .

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

Step 4.1.2

Move $- 2$ to the left of $x$ .

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

Step 4.1.3

Multiply $- 2$ by $- 2$ .

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

Step 4.2

Subtract $2 x$ from $- 2 x$ .

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

Step 5

Apply the distributive property.

$f (x) = 2 (- x^{2} - (- 4 x) - 1 \cdot 4 - 2)$

Step 6

Simplify.

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Step 6.1

Multiply $- 4$ by $- 1$ .

$f (x) = 2 (- x^{2} + 4 x - 1 \cdot 4 - 2)$

Step 6.2

Multiply $- 1$ by $4$ .

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

Step 7

Subtract $2$ from $- 4$ .

$f (x) = 2 (- x^{2} + 4 x - 6)$