Graph y<=-(x+1)^2+4

$y \leq - {(x + 1)}^{2} + 4$

Step 1

Simplify $- {(x + 1)}^{2} + 4$ .

Simplify each term.

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$y \leq - ((x + 1) (x + 1)) + 4$

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$y \leq - (x (x + 1) + 1 (x + 1)) + 4$

Apply the distributive property.

$y \leq - (x \cdot x + x \cdot 1 + 1 (x + 1)) + 4$

Apply the distributive property.

$y \leq - (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1) + 4$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $x$ by $1$ .

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

Multiply $1$ by $1$ .

$y \leq - (x^{2} + x + x + 1) + 4$

Add $x$ and $x$ .

$y \leq - (x^{2} + 2 x + 1) + 4$

Apply the distributive property.

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

Simplify.

Multiply $2$ by $- 1$ .

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

Multiply $- 1$ by $1$ .

$y \leq - x^{2} - 2 x - 1 + 4$

Add $- 1$ and $4$ .

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

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 $- x^{2} - 2 x + 3$ .

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

Step 4