Trigonometry Examples

$f (x) = 13 {(x - 14)}^{2}$

Step 1

Rewrite the function as an equation.

$y = 13 {(x - 14)}^{2}$

Step 2

Simplify $13 {(x - 14)}^{2}$ .

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Step 2.1

Rewrite ${(x - 14)}^{2}$ as $(x - 14) (x - 14)$ .

$y = 13 ((x - 14) (x - 14))$

Step 2.2

Expand $(x - 14) (x - 14)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$y = 13 (x (x - 14) - 14 (x - 14))$

Step 2.2.2

Apply the distributive property.

$y = 13 (x \cdot x + x \cdot - 14 - 14 (x - 14))$

Step 2.2.3

Apply the distributive property.

$y = 13 (x \cdot x + x \cdot - 14 - 14 x - 14 \cdot - 14)$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $x$ by $x$ .

$y = 13 (x^{2} + x \cdot - 14 - 14 x - 14 \cdot - 14)$

Step 2.3.1.2

Move $- 14$ to the left of $x$ .

$y = 13 (x^{2} - 14 \cdot x - 14 x - 14 \cdot - 14)$

Step 2.3.1.3

Multiply $- 14$ by $- 14$ .

$y = 13 (x^{2} - 14 x - 14 x + 196)$

Step 2.3.2

Subtract $14 x$ from $- 14 x$ .

$y = 13 (x^{2} - 28 x + 196)$

Step 2.4

Apply the distributive property.

$y = 13 x^{2} + 13 (- 28 x) + 13 \cdot 196$

Step 2.5

Simplify.

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Step 2.5.1

Multiply $- 28$ by $13$ .

$y = 13 x^{2} - 364 x + 13 \cdot 196$

Step 2.5.2

Multiply $13$ by $196$ .

$y = 13 x^{2} - 364 x + 2548$