Graph y>=-(x+2)^2-4

$y \geq - {(x + 2)}^{2} - 4$

Step 1

Simplify $- {(x + 2)}^{2} - 4$ .

Simplify each term.

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

$y \geq - ((x + 2) (x + 2)) - 4$

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

Apply the distributive property.

$y \geq - (x (x + 2) + 2 (x + 2)) - 4$

Apply the distributive property.

$y \geq - (x \cdot x + x \cdot 2 + 2 (x + 2)) - 4$

Apply the distributive property.

$y \geq - (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) - 4$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y \geq - (x^{2} + x \cdot 2 + 2 x + 2 \cdot 2) - 4$

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

$y \geq - (x^{2} + 2 \cdot x + 2 x + 2 \cdot 2) - 4$

Multiply $2$ by $2$ .

$y \geq - (x^{2} + 2 x + 2 x + 4) - 4$

Add $2 x$ and $2 x$ .

$y \geq - (x^{2} + 4 x + 4) - 4$

Apply the distributive property.

$y \geq - x^{2} - (4 x) - 1 \cdot 4 - 4$

Simplify.

Multiply $4$ by $- 1$ .

$y \geq - x^{2} - 4 x - 1 \cdot 4 - 4$

Multiply $- 1$ by $4$ .

$y \geq - x^{2} - 4 x - 4 - 4$

Subtract $4$ from $- 4$ .

$y \geq - x^{2} - 4 x - 8$

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 $- x^{2} - 4 x - 8$ .

$y \geq - x^{2} - 4 x - 8$

Step 4