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

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

Step 1

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

Rewrite ${(x + 4)}^{2}$ as $(x + 4) (x + 4)$ .

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

Expand $(x + 4) (x + 4)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $4$ to the left of $x$ .

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

Multiply $4$ by $4$ .

$y \geq - (x^{2} + 4 x + 4 x + 16)$

Add $4 x$ and $4 x$ .

$y \geq - (x^{2} + 8 x + 16)$

Apply the distributive property.

$y \geq - x^{2} - (8 x) - 1 \cdot 16$

Simplify.

Multiply $8$ by $- 1$ .

$y \geq - x^{2} - 8 x - 1 \cdot 16$

Multiply $- 1$ by $16$ .

$y \geq - x^{2} - 8 x - 16$

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 $- x^{2} - 8 x - 16$ .

$y \geq - x^{2} - 8 x - 16$

Step 4