Graph y=-2x(x+1)(x-2)

$y = - 2 x (x + 1) (x - 2)$

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

$f (- 1) = - 2 \cdot - 1 + 2 {(- 1)}^{2} + 4 (- 1)$

Multiply $- 2$ by $- 1$ .

$f (- 1) = 2 + 2 {(- 1)}^{2} + 4 (- 1)$

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

$f (- 1) = 2 + 2 \cdot 1 + 4 (- 1)$

Multiply $2$ by $1$ .

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

Multiply $4$ by $- 1$ .

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

Simplify by adding and subtracting.

Add $2$ and $2$ .

$f (- 1) = 4 - 4$

Subtract $4$ from $4$ .

$f (- 1) = 0$

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.

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

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = - 2 \cdot 1 + 2 {(1)}^{2} + 4 (1)$

Multiply $- 2$ by $1$ .

$f (1) = - 2 + 2 {(1)}^{2} + 4 (1)$

One to any power is one.

$f (1) = - 2 + 2 \cdot 1 + 4 (1)$

Multiply $2$ by $1$ .

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

Multiply $4$ by $1$ .

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

Simplify by adding numbers.

Add $- 2$ and $2$ .

$f (1) = 0 + 4$

Add $0$ and $4$ .

$f (1) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

$f (2) = - 2 \cdot 8 + 2 {(2)}^{2} + 4 (2)$

Multiply $- 2$ by $8$ .

$f (2) = - 16 + 2 {(2)}^{2} + 4 (2)$

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

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

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

$f (2) = - 16 + 2 {(2)}^{2} + 4 (2)$

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

$f (2) = - 16 + 2^{1 + 2} + 4 (2)$

Add $1$ and $2$ .

$f (2) = - 16 + 2^{3} + 4 (2)$

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

$f (2) = - 16 + 8 + 4 (2)$

Multiply $4$ by $2$ .

$f (2) = - 16 + 8 + 8$

Simplify by adding numbers.

Add $- 16$ and $8$ .

$f (2) = - 8 + 8$

Add $- 8$ and $8$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 3$ .

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

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

Simplify the result.

Simplify each term.

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

$f (3) = - 2 \cdot 27 + 2 {(3)}^{2} + 4 (3)$

Multiply $- 2$ by $27$ .

$f (3) = - 54 + 2 {(3)}^{2} + 4 (3)$

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

$f (3) = - 54 + 2 \cdot 9 + 4 (3)$

Multiply $2$ by $9$ .

$f (3) = - 54 + 18 + 4 (3)$

Multiply $4$ by $3$ .

$f (3) = - 54 + 18 + 12$

Simplify by adding numbers.

Add $- 54$ and $18$ .

$f (3) = - 36 + 12$

Add $- 36$ and $12$ .

$f (3) = - 24$

The final answer is $- 24$ .

$- 24$

Convert $- 24$ to decimal.

$y = - 24$

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

$\begin{array}{c} x & y \\ - 1 & 0 \\ 0 & 0 \\ 1 & 4 \\ 2 & 0 \\ 3 & - 24 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 1 & 0 \\ 0 & 0 \\ 1 & 4 \\ 2 & 0 \\ 3 & - 24 \end{array}$

Graph y=-2x(x+1)(x-2)

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