Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

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

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

Step 1.1.2

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

Tap for more steps...

Step 1.1.2.1

Apply the distributive property.

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

Step 1.1.2.2

Apply the distributive property.

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

Step 1.1.2.3

Apply the distributive property.

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

Step 1.1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.1.3.1

Simplify each term.

Tap for more steps...

Step 1.1.3.1.1

Multiply $x$ by $x$ .

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

Step 1.1.3.1.2

Multiply $x$ by $1$ .

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

Step 1.1.3.1.3

Multiply $x$ by $1$ .

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

Step 1.1.3.1.4

Multiply $1$ by $1$ .

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

Step 1.1.3.2

Add $x$ and $x$ .

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

Step 1.1.4

Apply the distributive property.

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

Step 1.1.5

Simplify.

Tap for more steps...

Step 1.1.5.1

Multiply $2$ by $- 1$ .

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

Step 1.1.5.2

Multiply $- 1$ by $1$ .

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

Step 1.2

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