Graph f(x)=-2x(x^2-9)

$f (x) = - 2 x (x^{2} - 9)$

Find the point at $x = - 2$ .

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

$f (- 2) = - 2 {(- 2)}^{3} + 18 (- 2)$

Simplify the result.

Simplify each term.

Multiply $- 2$ by ${(- 2)}^{3}$ by adding the exponents.

Multiply $- 2$ by ${(- 2)}^{3}$ .

Raise $- 2$ to the power of $1$ .

$f (- 2) = (- 2) {(- 2)}^{3} + 18 (- 2)$

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

$f (- 2) = {(- 2)}^{1 + 3} + 18 (- 2)$

Add $1$ and $3$ .

$f (- 2) = {(- 2)}^{4} + 18 (- 2)$

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

$f (- 2) = 16 + 18 (- 2)$

Multiply $18$ by $- 2$ .

$f (- 2) = 16 - 36$

Subtract $36$ from $16$ .

$f (- 2) = - 20$

The final answer is $- 20$ .

$- 20$

Convert $- 20$ to decimal.

$y = - 20$

Find the point at $x = - 1$ .

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

$f (- 1) = - 2 {(- 1)}^{3} + 18 (- 1)$

Simplify the result.

Simplify each term.

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

$f (- 1) = - 2 \cdot - 1 + 18 (- 1)$

Multiply $- 2$ by $- 1$ .

$f (- 1) = 2 + 18 (- 1)$

Multiply $18$ by $- 1$ .

$f (- 1) = 2 - 18$

Subtract $18$ from $2$ .

$f (- 1) = - 16$

The final answer is $- 16$ .

$- 16$

Convert $- 16$ to decimal.

$y = - 16$

Find the point at $x = 0$ .

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

$f (0) = - 2 {(0)}^{3} + 18 (0)$

Simplify the result.

Simplify each term.

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

$f (0) = - 2 \cdot 0 + 18 (0)$

Multiply $- 2$ by $0$ .

$f (0) = 0 + 18 (0)$

Multiply $18$ by $0$ .

$f (0) = 0 + 0$

Add $0$ and $0$ .

$f (0) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 1$ .

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

$f (1) = - 2 {(1)}^{3} + 18 (1)$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = - 2 \cdot 1 + 18 (1)$

Multiply $- 2$ by $1$ .

$f (1) = - 2 + 18 (1)$

Multiply $18$ by $1$ .

$f (1) = - 2 + 18$

Add $- 2$ and $18$ .

$f (1) = 16$

The final answer is $16$ .

$16$

Convert $16$ to decimal.

$y = 16$

Find the point at $x = 2$ .

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

$f (2) = - 2 {(2)}^{3} + 18 (2)$

Simplify the result.

Simplify each term.

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

$f (2) = - 2 \cdot 8 + 18 (2)$

Multiply $- 2$ by $8$ .

$f (2) = - 16 + 18 (2)$

Multiply $18$ by $2$ .

$f (2) = - 16 + 36$

Add $- 16$ and $36$ .

$f (2) = 20$

The final answer is $20$ .

$20$

Convert $20$ to decimal.

$y = 20$

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

$\begin{array}{c} x & y \\ - 2 & - 20 \\ - 1 & - 16 \\ 0 & 0 \\ 1 & 16 \\ 2 & 20 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 2 & - 20 \\ - 1 & - 16 \\ 0 & 0 \\ 1 & 16 \\ 2 & 20 \end{array}$

Graph f(x)=-2x(x^2-9)

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