Pre-Algebra Examples

$f (x) = - 0.5 {(x + 1)}^{2} + 2$

Step 1

Rewrite the function as an equation.

$y = - 0.5 {(x + 1)}^{2} + 2$

Step 2

Simplify $- 0.5 {(x + 1)}^{2} + 2$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$y = - 0.5 ((x + 1) (x + 1)) + 2$

Step 2.1.2

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

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Step 2.1.2.1

Apply the distributive property.

$y = - 0.5 (x (x + 1) + 1 (x + 1)) + 2$

Step 2.1.2.2

Apply the distributive property.

$y = - 0.5 (x \cdot x + x \cdot 1 + 1 (x + 1)) + 2$

Step 2.1.2.3

Apply the distributive property.

$y = - 0.5 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1) + 2$

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

$y = - 0.5 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1) + 2$

Step 2.1.3.1.2

Multiply $x$ by $1$ .

$y = - 0.5 (x^{2} + x + 1 x + 1 \cdot 1) + 2$

Step 2.1.3.1.3

Multiply $x$ by $1$ .

$y = - 0.5 (x^{2} + x + x + 1 \cdot 1) + 2$

Step 2.1.3.1.4

Multiply $1$ by $1$ .

$y = - 0.5 (x^{2} + x + x + 1) + 2$

Step 2.1.3.2

Add $x$ and $x$ .

$y = - 0.5 (x^{2} + 2 x + 1) + 2$

Step 2.1.4

Apply the distributive property.

$y = - 0.5 x^{2} - 0.5 (2 x) - 0.5 \cdot 1 + 2$

Step 2.1.5

Simplify.

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Step 2.1.5.1

Multiply $2$ by $- 0.5$ .

$y = - 0.5 x^{2} - 1 x - 0.5 \cdot 1 + 2$

Step 2.1.5.2

Multiply $- 0.5$ by $1$ .

$y = - 0.5 x^{2} - 1 x - 0.5 + 2$

Step 2.1.6

Rewrite $- 1 x$ as $- x$ .

$y = - 0.5 x^{2} - x - 0.5 + 2$

Step 2.2

Add $- 0.5$ and $2$ .

$y = - 0.5 x^{2} - x + 1.5$