Algebra Examples

$y = - \frac{1}{2} {(x - 3)}^{3}$

Step 1

Find the point at $x = 1$ .

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Step 1.1

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

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

Step 1.2

Simplify the result.

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Step 1.2.1

Simplify the numerator.

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Step 1.2.1.1

Subtract $3$ from $1$ .

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

Step 1.2.1.2

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

$f (1) = - \frac{- 8}{2}$

Step 1.2.2

Simplify the expression.

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Step 1.2.2.1

Divide $- 8$ by $2$ .

$f (1) = 4$

Step 1.2.2.2

Multiply $- 1$ by $- 4$ .

$f (1) = 4$

Step 1.2.3

The final answer is $4$ .

$4$

Step 1.3

Convert $4$ to decimal.

$y = 4$

Step 2

Find the point at $x = 3$ .

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Step 2.1

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

$f (3) = - \frac{{((3) - 3)}^{3}}{2}$

Step 2.2

Simplify the result.

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Step 2.2.1

Simplify the numerator.

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Step 2.2.1.1

Subtract $3$ from $3$ .

$f (3) = - \frac{0^{3}}{2}$

Step 2.2.1.2

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

$f (3) = - \frac{0}{2}$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Divide $0$ by $2$ .

$f (3) = - 0$

Step 2.2.2.2

Multiply $- 1$ by $0$ .

$f (3) = 0$

Step 2.2.3

The final answer is $0$ .

$0$

Step 2.3

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 5$ .

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Step 3.1

Replace the variable $x$ with $5$ in the expression.

$f (5) = - \frac{{((5) - 3)}^{3}}{2}$

Step 3.2

Simplify the result.

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Step 3.2.1

Simplify the numerator.

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Step 3.2.1.1

Subtract $3$ from $5$ .

$f (5) = - \frac{2^{3}}{2}$

Step 3.2.1.2

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

$f (5) = - \frac{8}{2}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Divide $8$ by $2$ .

$f (5) = - 1 \cdot 4$

Step 3.2.2.2

Multiply $- 1$ by $4$ .

$f (5) = - 4$

Step 3.2.3

The final answer is $- 4$ .

$- 4$

Step 3.3

Convert $- 4$ to decimal.

$y = - 4$

Step 4

Find the point at $x = 2$ .

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Step 4.1

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

$f (2) = - \frac{{((2) - 3)}^{3}}{2}$

Step 4.2

Simplify the result.

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Step 4.2.1

Simplify the numerator.

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Step 4.2.1.1

Subtract $3$ from $2$ .

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

Step 4.2.1.2

Raise $- 1$ to the power of $3$ .

$f (2) = - \frac{- 1}{2}$

Step 4.2.2

Move the negative in front of the fraction.

$f (2) = \frac{1}{2}$

Step 4.2.3

The final answer is $\frac{1}{2}$ .

$\frac{1}{2}$

Step 4.3

Convert $\frac{1}{2}$ to decimal.

$y = 0.5$

Step 5

Find the point at $x = 4$ .

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Step 5.1

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

$f (4) = - \frac{{((4) - 3)}^{3}}{2}$

Step 5.2

Simplify the result.

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Step 5.2.1

Simplify the numerator.

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Step 5.2.1.1

Subtract $3$ from $4$ .

$f (4) = - \frac{1^{3}}{2}$

Step 5.2.1.2

One to any power is one.

$f (4) = - \frac{1}{2}$

Step 5.2.2

The final answer is $- \frac{1}{2}$ .

$- \frac{1}{2}$

Step 5.3

Convert $- \frac{1}{2}$ to decimal.

$y = - 0.5$

Step 6

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

$\begin{array}{c} x & y \\ 1 & 4 \\ 2 & 0.5 \\ 3 & 0 \\ 4 & - 0.5 \\ 5 & - 4 \end{array}$

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

$\begin{array}{c} x & y \\ 1 & 4 \\ 2 & 0.5 \\ 3 & 0 \\ 4 & - 0.5 \\ 5 & - 4 \end{array}$

Step 8