Algebra Examples

$y \leq {(x - 3)}^{2} + 3$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$y \leq (x - 3) (x - 3) + 3$

Step 1.1.2

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

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Step 1.1.2.1

Apply the distributive property.

$y \leq x (x - 3) - 3 (x - 3) + 3$

Step 1.1.2.2

Apply the distributive property.

$y \leq x \cdot x + x \cdot - 3 - 3 (x - 3) + 3$

Step 1.1.2.3

Apply the distributive property.

$y \leq x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3 + 3$

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 $x$ .

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

Step 1.1.3.1.2

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

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

Step 1.1.3.1.3

Multiply $- 3$ by $- 3$ .

$y \leq x^{2} - 3 x - 3 x + 9 + 3$

Step 1.1.3.2

Subtract $3 x$ from $- 3 x$ .

$y \leq x^{2} - 6 x + 9 + 3$

Step 1.2

Add $9$ and $3$ .

$y \leq x^{2} - 6 x + 12$

Step 2

The equation is not linear, so a constant slope does not exist.

Not Linear

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $x^{2} - 6 x + 12$ .

$y \leq x^{2} - 6 x + 12$

Step 4