Graph f(x)=-2x(x-1)(x+4)

$f (x) = - 2 x (x - 1) (x + 4)$

Step 1

Find the point at $x = - 3$ .

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

$f (- 3) = - 2 {(- 3)}^{3} - 6 {(- 3)}^{2} + 8 (- 3)$

Simplify the result.

Simplify each term.

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

$f (- 3) = - 2 \cdot - 27 - 6 {(- 3)}^{2} + 8 (- 3)$

Multiply $- 2$ by $- 27$ .

$f (- 3) = 54 - 6 {(- 3)}^{2} + 8 (- 3)$

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

$f (- 3) = 54 - 6 \cdot 9 + 8 (- 3)$

Multiply $- 6$ by $9$ .

$f (- 3) = 54 - 54 + 8 (- 3)$

Multiply $8$ by $- 3$ .

$f (- 3) = 54 - 54 - 24$

Simplify by subtracting numbers.

Subtract $54$ from $54$ .

$f (- 3) = 0 - 24$

Subtract $24$ from $0$ .

$f (- 3) = - 24$

The final answer is $- 24$ .

$- 24$

Convert $- 24$ to decimal.

$y = - 24$

Step 2

Find the point at $x = - 1$ .

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

$f (- 1) = - 2 {(- 1)}^{3} - 6 {(- 1)}^{2} + 8 (- 1)$

Simplify the result.

Simplify each term.

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

$f (- 1) = - 2 \cdot - 1 - 6 {(- 1)}^{2} + 8 (- 1)$

Multiply $- 2$ by $- 1$ .

$f (- 1) = 2 - 6 {(- 1)}^{2} + 8 (- 1)$

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

$f (- 1) = 2 - 6 \cdot 1 + 8 (- 1)$

Multiply $- 6$ by $1$ .

$f (- 1) = 2 - 6 + 8 (- 1)$

Multiply $8$ by $- 1$ .

$f (- 1) = 2 - 6 - 8$

Simplify by subtracting numbers.

Subtract $6$ from $2$ .

$f (- 1) = - 4 - 8$

Subtract $8$ from $- 4$ .

$f (- 1) = - 12$

The final answer is $- 12$ .

$- 12$

Convert $- 12$ to decimal.

$y = - 12$

Step 3

Find the point at $x = 0$ .

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

$f (0) = - 2 {(0)}^{3} - 6 {(0)}^{2} + 8 (0)$

Simplify the result.

Simplify each term.

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

$f (0) = - 2 \cdot 0 - 6 {(0)}^{2} + 8 (0)$

Multiply $- 2$ by $0$ .

$f (0) = 0 - 6 {(0)}^{2} + 8 (0)$

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

$f (0) = 0 - 6 \cdot 0 + 8 (0)$

Multiply $- 6$ by $0$ .

$f (0) = 0 + 0 + 8 (0)$

Multiply $8$ by $0$ .

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

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0$

Add $0$ and $0$ .

$f (0) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 4

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

$\begin{array}{c} x & y \\ - 3 & - 24 \\ - 2 & - 24 \\ - 1 & - 12 \\ 0 & 0 \\ 1 & 0 \end{array}$

Step 5

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 3 & - 24 \\ - 2 & - 24 \\ - 1 & - 12 \\ 0 & 0 \\ 1 & 0 \end{array}$

Step 6

Graph f(x)=-2x(x-1)(x+4)

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