Graph x^3+x^2-2x

$x^{3} + x^{2} - 2 x$

Step 1

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

Multiply $- 2$ by $- 2$ .

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

Simplify by adding numbers.

Add $- 8$ and $4$ .

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

Add $- 4$ and $4$ .

$f (- 2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 2

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

Multiply $- 2$ by $- 1$ .

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

Simplify by adding numbers.

Add $- 1$ and $1$ .

$f (- 1) = 0 + 2$

Add $0$ and $2$ .

$f (- 1) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Step 3

Find the point at $x = 0$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

Multiply $- 2$ 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

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

Multiply $- 2$ by $2$ .

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

Simplify by adding and subtracting.

Add $8$ and $4$ .

$f (2) = 12 - 4$

Subtract $4$ from $12$ .

$f (2) = 8$

The final answer is $8$ .

$8$

Convert $8$ to decimal.

$y = 8$

Step 5

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

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

Step 6

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

Falls to the left and rises to the right

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

Step 7

Graph x^3+x^2-2x

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