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

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

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

Multiply $- 2$ by $1$ .

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

Multiply $- 1$ by $- 1$ .

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

Simplify by adding and subtracting.

Subtract $2$ from $- 1$ .

$f (- 1) = - 3 + 1 + 2$

Add $- 3$ and $1$ .

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

Add $- 2$ and $2$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 0$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

Multiply $- 2$ by $0$ .

$f (0) = 0 + 0 - (0) + 2$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 0 + 0 + 2$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0 + 2$

Add $0$ and $0$ .

$f (0) = 0 + 2$

Add $0$ and $2$ .

$f (0) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify each term.

One to any power is one.

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

One to any power is one.

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

Multiply $- 2$ by $1$ .

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

Multiply $- 1$ by $1$ .

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

Simplify by adding and subtracting.

Subtract $2$ from $1$ .

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

Subtract $1$ from $- 1$ .

$f (1) = - 2 + 2$

Add $- 2$ and $2$ .

$f (1) = 0$

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.

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

Simplify the result.

Simplify each term.

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

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

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

$f (3) = 27 - 2 \cdot 9 - (3) + 2$

Multiply $- 2$ by $9$ .

$f (3) = 27 - 18 - (3) + 2$

Multiply $- 1$ by $3$ .

$f (3) = 27 - 18 - 3 + 2$

Simplify by adding and subtracting.

Subtract $18$ from $27$ .

$f (3) = 9 - 3 + 2$

Subtract $3$ from $9$ .

$f (3) = 6 + 2$

Add $6$ and $2$ .

$f (3) = 8$

The final answer is $8$ .

$8$

Convert $8$ to decimal.

$y = 8$

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

$\begin{array}{c} x & y \\ - 1 & 0 \\ 0 & 2 \\ 1 & 0 \\ 2 & 0 \\ 3 & 8 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 1 & 0 \\ 0 & 2 \\ 1 & 0 \\ 2 & 0 \\ 3 & 8 \end{array}$

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

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