Algebra Examples

$y \geq {(x + 2)}^{2} + 1$

Step 1

Simplify ${(x + 2)}^{2} + 1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$y \geq (x + 2) (x + 2) + 1$

Step 1.1.2

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

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Step 1.1.2.1

Apply the distributive property.

$y \geq x (x + 2) + 2 (x + 2) + 1$

Step 1.1.2.2

Apply the distributive property.

$y \geq x \cdot x + x \cdot 2 + 2 (x + 2) + 1$

Step 1.1.2.3

Apply the distributive property.

$y \geq x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2 + 1$

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 $x$ .

$y \geq x^{2} + x \cdot 2 + 2 x + 2 \cdot 2 + 1$

Step 1.1.3.1.2

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

$y \geq x^{2} + 2 \cdot x + 2 x + 2 \cdot 2 + 1$

Step 1.1.3.1.3

Multiply $2$ by $2$ .

$y \geq x^{2} + 2 x + 2 x + 4 + 1$

Step 1.1.3.2

Add $2 x$ and $2 x$ .

$y \geq x^{2} + 4 x + 4 + 1$

Step 1.2

Add $4$ and $1$ .

$y \geq x^{2} + 4 x + 5$

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 above the boundary line since $y$ is greater than $x^{2} + 4 x + 5$ .

$y \geq x^{2} + 4 x + 5$

Step 4