Algebra Examples

$h (x) = - \frac{5}{6} x^{3}$

Step 1

Write $h (x) = - \frac{5}{6} x^{3}$ as an equation.

$y = - \frac{5}{6} x^{3}$

Step 2

Simplify $- \frac{5}{6} x^{3}$ .

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Step 2.1

Combine $x^{3}$ and $\frac{5}{6}$ .

$y = - \frac{x^{3} \cdot 5}{6}$

Step 2.2

Move $5$ to the left of $x^{3}$ .

$y = - \frac{5 x^{3}}{6}$

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = - \frac{5 \cdot 0^{3}}{6}$

Step 4.2

Remove parentheses.

$y = - \frac{5 {(0)}^{3}}{6}$

Step 4.3

Simplify $- \frac{5 {(0)}^{3}}{6}$ .

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Step 4.3.1

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

$y = - \frac{5 \cdot 0}{6}$

Step 4.3.2

Multiply $5$ by $0$ .

$y = - \frac{0}{6}$

Step 4.3.3

Divide $0$ by $6$ .

$y = - 0$

Step 4.3.4

Multiply $- 1$ by $0$ .

$y = 0$

Step 4.4

Use the $x$ and $y$ values to form the ordered pair.

$(0, 0)$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = - \frac{5 \cdot 1^{3}}{6}$

Step 5.2

Remove parentheses.

$y = - \frac{5 {(1)}^{3}}{6}$

Step 5.3

Simplify $- \frac{5 {(1)}^{3}}{6}$ .

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Step 5.3.1

One to any power is one.

$y = - \frac{5 \cdot 1}{6}$

Step 5.3.2

Multiply $5$ by $1$ .

$y = - \frac{5}{6}$

Step 5.4

Use the $x$ and $y$ values to form the ordered pair.

$(1, - \frac{5}{6})$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 6.1

Remove parentheses.

$y = - \frac{5 \cdot 2^{3}}{6}$

Step 6.2

Remove parentheses.

$y = - \frac{5 {(2)}^{3}}{6}$

Step 6.3

Simplify $- \frac{5 {(2)}^{3}}{6}$ .

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Step 6.3.1

Simplify the expression.

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Step 6.3.1.1

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

$y = - \frac{5 \cdot 8}{6}$

Step 6.3.1.2

Multiply $5$ by $8$ .

$y = - \frac{40}{6}$

Step 6.3.2

Cancel the common factor of $40$ and $6$ .

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Step 6.3.2.1

Factor $2$ out of $40$ .

$y = - \frac{2 (20)}{6}$

Step 6.3.2.2

Cancel the common factors.

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Step 6.3.2.2.1

Factor $2$ out of $6$ .

$y = - \frac{2 \cdot 20}{2 \cdot 3}$

Step 6.3.2.2.2

Cancel the common factor.

$y = - \frac{2 \cdot 20}{2 \cdot 3}$

Step 6.3.2.2.3

Rewrite the expression.

$y = - \frac{20}{3}$

Step 6.4

Use the $x$ and $y$ values to form the ordered pair.

$(2, - \frac{20}{3})$

Step 7

These are three possible solutions to the equation.

$(0, 0), (1, - \frac{5}{6}), (2, - \frac{20}{3})$

Step 8