Algebra Examples

$y = {(x - 5)}^{2} - 3$

Step 1

Simplify ${(x - 5)}^{2} - 3$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

$y = (x - 5) (x - 5) - 3$

Step 1.1.2

Expand $(x - 5) (x - 5)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$y = x (x - 5) - 5 (x - 5) - 3$

Step 1.1.2.2

Apply the distributive property.

$y = x \cdot x + x \cdot - 5 - 5 (x - 5) - 3$

Step 1.1.2.3

Apply the distributive property.

$y = x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5 - 3$

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 $x$ .

$y = x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5 - 3$

Step 1.1.3.1.2

Move $- 5$ to the left of $x$ .

$y = x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5 - 3$

Step 1.1.3.1.3

Multiply $- 5$ by $- 5$ .

$y = x^{2} - 5 x - 5 x + 25 - 3$

Step 1.1.3.2

Subtract $5 x$ from $- 5 x$ .

$y = x^{2} - 10 x + 25 - 3$

Step 1.2

Subtract $3$ from $25$ .

$y = x^{2} - 10 x + 22$

Step 2

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

Increasing on: $(5, \infty)$

Decreasing on: $(- \infty, 5)$

Step 3