Algebra Examples

$y = {(x - 9)}^{2} - 5$

Step 1

Simplify ${(x - 9)}^{2} - 5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x - 9)}^{2}$ as $(x - 9) (x - 9)$ .

$y = (x - 9) (x - 9) - 5$

Step 1.1.2

Expand $(x - 9) (x - 9)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$y = x (x - 9) - 9 (x - 9) - 5$

Step 1.1.2.2

Apply the distributive property.

$y = x \cdot x + x \cdot - 9 - 9 (x - 9) - 5$

Step 1.1.2.3

Apply the distributive property.

$y = x \cdot x + x \cdot - 9 - 9 x - 9 \cdot - 9 - 5$

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 9 - 9 x - 9 \cdot - 9 - 5$

Step 1.1.3.1.2

Move $- 9$ to the left of $x$ .

$y = x^{2} - 9 \cdot x - 9 x - 9 \cdot - 9 - 5$

Step 1.1.3.1.3

Multiply $- 9$ by $- 9$ .

$y = x^{2} - 9 x - 9 x + 81 - 5$

Step 1.1.3.2

Subtract $9 x$ from $- 9 x$ .

$y = x^{2} - 18 x + 81 - 5$

Step 1.2

Subtract $5$ from $81$ .

$y = x^{2} - 18 x + 76$

Step 2

Graph the equation in order to determine the intervals over which it is increasing or decreasing.

Increasing on: $(9, \infty)$

Decreasing on: $(- \infty, 9)$

Step 3