Graph Using a Table of Values y=-3/2x^3

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

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

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

Step 2

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

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

$y = - \frac{3}{2} \cdot - 8$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$y = \frac{- 3}{2} \cdot - 8$

Factor $2$ out of $- 8$ .

$y = \frac{- 3}{2} \cdot (2 (- 4))$

Cancel the common factor.

$y = \frac{- 3}{2} \cdot (2 \cdot - 4)$

Rewrite the expression.

$y = - 3 \cdot - 4$

Multiply $- 3$ by $- 4$ .

$y = 12$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

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

Step 4

Simplify $- \frac{3}{2} \cdot {(- 1)}^{3}$ .

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

Move ${(- 1)}^{3}$ .

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

Multiply ${(- 1)}^{3}$ by $- 1$ .

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

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $3$ and $1$ .

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

Raise $- 1$ to the power of $4$ .

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

Multiply $\frac{3}{2}$ by $1$ .

$y = \frac{3}{2}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{3}{2} \cdot 0^{3}$

Remove parentheses.

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

Simplify $- \frac{3}{2} \cdot {(0)}^{3}$ .

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

$y = - \frac{3}{2} \cdot 0$

Multiply $- \frac{3}{2} \cdot 0$ .

Multiply $0$ by $- 1$ .

$y = 0 (\frac{3}{2})$

Multiply $0$ by $\frac{3}{2}$ .

$y = 0$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{3}{2} \cdot 1^{3}$

Remove parentheses.

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

Simplify $- \frac{3}{2} \cdot {(1)}^{3}$ .

One to any power is one.

$y = - \frac{3}{2} \cdot 1$

Multiply $- 1$ by $1$ .

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

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Factor $2$ out of ${(2)}^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = - 3 \cdot 2^{2}$

Simplify the expression.

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

$y = - 3 \cdot 4$

Multiply $- 3$ by $4$ .

$y = - 12$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & 12 \\ - 1 & \frac{3}{2} \\ 0 & 0 \\ 1 & - \frac{3}{2} \\ 2 & - 12 \end{array}$

Step 12

Graph Using a Table of Values y=-3/2x^3

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