Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

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

Step 1.3.1.2

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

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

Step 1.3.1.3

Multiply $4$ by $4$ .

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

Step 1.3.2

Add $4 x$ and $4 x$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Simplify.

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Step 1.5.1

Multiply $8$ by $- 1$ .

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

Step 1.5.2

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