Graph y<=(x+2)^2

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

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

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

$y \leq (x + 2) (x + 2)$

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

Apply the distributive property.

$y \leq x (x + 2) + 2 (x + 2)$

Apply the distributive property.

$y \leq x \cdot x + x \cdot 2 + 2 (x + 2)$

Apply the distributive property.

$y \leq x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $2$ by $2$ .

$y \leq x^{2} + 2 x + 2 x + 4$

Add $2 x$ and $2 x$ .

$y \leq x^{2} + 4 x + 4$

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

Not Linear

Graph a solid line, then shade the area below the boundary line since $y$ is less than $x^{2} + 4 x + 4$ .

$y \leq x^{2} + 4 x + 4$