Pre-Algebra Examples

$f (x) = - 0.5 x {(x + 4)}^{2} - 2$

Step 1

Find the point at $x = - 4$ .

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Step 1.1

Replace the variable $x$ with $- 4$ in the expression.

$f (- 4) = - 0.5 \cdot - 4 {((- 4) + 4)}^{2} - 2$

Step 1.2

Simplify the result.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $- 0.5$ by $- 4$ .

$f (- 4) = 2 {((- 4) + 4)}^{2} - 2$

Step 1.2.1.2

Add $- 4$ and $4$ .

$f (- 4) = 2 \cdot 0^{2} - 2$

Step 1.2.1.3

Raising $0$ to any positive power yields $0$ .

$f (- 4) = 2 \cdot 0 - 2$

Step 1.2.1.4

Multiply $2$ by $0$ .

$f (- 4) = 0 - 2$

Step 1.2.2

Subtract $2$ from $0$ .

$f (- 4) = - 2$

Step 1.2.3

The final answer is $- 2$ .

$- 2$

Step 1.3

Convert $- 2$ to decimal.

$y = - 2$

Step 2

Find the point at $x = - 2$ .

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Step 2.1

Replace the variable $x$ with $- 2$ in the expression.

$f (- 2) = - 0.5 \cdot - 2 {((- 2) + 4)}^{2} - 2$

Step 2.2

Simplify the result.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $- 0.5$ by $- 2$ .

$f (- 2) = 1 {((- 2) + 4)}^{2} - 2$

Step 2.2.1.2

Multiply ${((- 2) + 4)}^{2}$ by $1$ .

$f (- 2) = {((- 2) + 4)}^{2} - 2$

Step 2.2.1.3

Add $- 2$ and $4$ .

$f (- 2) = 2^{2} - 2$

Step 2.2.1.4

Raise $2$ to the power of $2$ .

$f (- 2) = 4 - 2$

Step 2.2.2

Subtract $2$ from $4$ .

$f (- 2) = 2$

Step 2.2.3

The final answer is $2$ .

$2$

Step 2.3

Convert $2$ to decimal.

$y = 2$

Step 3

Find the point at $x = 0$ .

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Step 3.1

Replace the variable $x$ with $0$ in the expression.

$f (0) = - 0.5 \cdot 0 {((0) + 4)}^{2} - 2$

Step 3.2

Simplify the result.

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Multiply $- 0.5$ by $0$ .

$f (0) = 0 {((0) + 4)}^{2} - 2$

Step 3.2.1.2

Add $0$ and $4$ .

$f (0) = 0 \cdot 4^{2} - 2$

Step 3.2.1.3

Raise $4$ to the power of $2$ .

$f (0) = 0 \cdot 16 - 2$

Step 3.2.1.4

Multiply $0$ by $16$ .

$f (0) = 0 - 2$

Step 3.2.2

Subtract $2$ from $0$ .

$f (0) = - 2$

Step 3.2.3

The final answer is $- 2$ .

$- 2$

Step 3.3

Convert $- 2$ to decimal.

$y = - 2$

Step 4

Find the point at $x = - 3$ .

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Step 4.1

Replace the variable $x$ with $- 3$ in the expression.

$f (- 3) = - 0.5 \cdot - 3 {((- 3) + 4)}^{2} - 2$

Step 4.2

Simplify the result.

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

Multiply $- 0.5$ by $- 3$ .

$f (- 3) = 1.5 {((- 3) + 4)}^{2} - 2$

Step 4.2.1.2

Add $- 3$ and $4$ .

$f (- 3) = 1.5 \cdot 1^{2} - 2$

Step 4.2.1.3

One to any power is one.

$f (- 3) = 1.5 \cdot 1 - 2$

Step 4.2.1.4

Multiply $1.5$ by $1$ .

$f (- 3) = 1.5 - 2$

Step 4.2.2

Subtract $2$ from $1.5$ .

$f (- 3) = - 0.5$

Step 4.2.3

The final answer is $- 0.5$ .

$- 0.5$

Step 5

Find the point at $x = - 1$ .

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Step 5.1

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = - 0.5 \cdot - 1 {((- 1) + 4)}^{2} - 2$

Step 5.2

Simplify the result.

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Multiply $- 0.5$ by $- 1$ .

$f (- 1) = 0.5 {((- 1) + 4)}^{2} - 2$

Step 5.2.1.2

Add $- 1$ and $4$ .

$f (- 1) = 0.5 \cdot 3^{2} - 2$

Step 5.2.1.3

Raise $3$ to the power of $2$ .

$f (- 1) = 0.5 \cdot 9 - 2$

Step 5.2.1.4

Multiply $0.5$ by $9$ .

$f (- 1) = 4.5 - 2$

Step 5.2.2

Subtract $2$ from $4.5$ .

$f (- 1) = 2.5$

Step 5.2.3

The final answer is $2.5$ .

$2.5$

Step 6

The cubic function can be graphed using the function behavior and the points.

$\begin{array}{c} x & y \\ - 4 & - 2 \\ - 3 & - 0.5 \\ - 2 & 2 \\ - 1 & 2.5 \\ 0 & - 2 \end{array}$

Step 7

The cubic function can be graphed using the function behavior and the selected points.

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 4 & - 2 \\ - 3 & - 0.5 \\ - 2 & 2 \\ - 1 & 2.5 \\ 0 & - 2 \end{array}$

Step 8