Graph y=-x^3+2x^2+x-2

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

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.

Remove parentheses.

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

Simplify each term.

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

Multiply $- 1$ by ${(- 1)}^{3}$ .

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

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

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

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

Add $1$ and $3$ .

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

Raise $- 1$ to the power of $4$ .

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

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

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

Multiply $2$ by $1$ .

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

Simplify by adding and subtracting.

Add $1$ and $2$ .

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

Subtract $1$ from $3$ .

$f (- 1) = 2 - 2$

Subtract $2$ from $2$ .

$f (- 1) = 0$

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.

Remove parentheses.

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

Simplify each term.

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

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

Multiply $- 1$ by $0$ .

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

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

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

Multiply $2$ by $0$ .

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

Simplify by adding and subtracting.

Add $0$ and $0$ .

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

Add $0$ and $0$ .

$f (0) = 0 - 2$

Subtract $2$ from $0$ .

$f (0) = - 2$

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.

Remove parentheses.

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

Simplify each term.

One to any power is one.

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

Multiply $- 1$ by $1$ .

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

One to any power is one.

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

Multiply $2$ by $1$ .

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

Simplify by adding and subtracting.

Add $- 1$ and $2$ .

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

Add $1$ and $1$ .

$f (1) = 2 - 2$

Subtract $2$ from $2$ .

$f (1) = 0$

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.

Remove parentheses.

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

Simplify each term.

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

$f (3) = - 1 \cdot 27 + 2 {(3)}^{2} + 3 - 2$

Multiply $- 1$ by $27$ .

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

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

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

Multiply $2$ by $9$ .

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

Simplify by adding and subtracting.

Add $- 27$ and $18$ .

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

Add $- 9$ and $3$ .

$f (3) = - 6 - 2$

Subtract $2$ from $- 6$ .

$f (3) = - 8$

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.

Rises to the left and falls to the right

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

Graph y=-x^3+2x^2+x-2

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