Graph -(x+3)(x+1)(x-2)

$- (x + 3) (x + 1) (x - 2)$

Find the point at $x = - 2$ .

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

$f (- 2) = - {(- 2)}^{3} - 2 {(- 2)}^{2} + 5 (- 2) + 6$

Simplify the result.

Simplify each term.

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

$f (- 2) = 8 - 2 {(- 2)}^{2} + 5 (- 2) + 6$

Multiply $- 1$ by $- 8$ .

$f (- 2) = 8 - 2 {(- 2)}^{2} + 5 (- 2) + 6$

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

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

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

$f (- 2) = 8 + (- 2) {(- 2)}^{2} + 5 (- 2) + 6$

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

$f (- 2) = 8 + {(- 2)}^{1 + 2} + 5 (- 2) + 6$

Add $1$ and $2$ .

$f (- 2) = 8 + {(- 2)}^{3} + 5 (- 2) + 6$

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

$f (- 2) = 8 - 8 + 5 (- 2) + 6$

Multiply $5$ by $- 2$ .

$f (- 2) = 8 - 8 - 10 + 6$

Simplify by adding and subtracting.

Subtract $8$ from $8$ .

$f (- 2) = 0 - 10 + 6$

Subtract $10$ from $0$ .

$f (- 2) = - 10 + 6$

Add $- 10$ and $6$ .

$f (- 2) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Find the point at $x = - 1$ .

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

$f (- 1) = - {(- 1)}^{3} - 2 {(- 1)}^{2} + 5 (- 1) + 6$

Simplify the result.

Simplify each term.

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

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

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

$f (- 1) = (- 1) {(- 1)}^{3} - 2 {(- 1)}^{2} + 5 (- 1) + 6$

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

$f (- 1) = {(- 1)}^{1 + 3} - 2 {(- 1)}^{2} + 5 (- 1) + 6$

Add $1$ and $3$ .

$f (- 1) = {(- 1)}^{4} - 2 {(- 1)}^{2} + 5 (- 1) + 6$

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

$f (- 1) = 1 - 2 {(- 1)}^{2} + 5 (- 1) + 6$

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

$f (- 1) = 1 - 2 \cdot 1 + 5 (- 1) + 6$

Multiply $- 2$ by $1$ .

$f (- 1) = 1 - 2 + 5 (- 1) + 6$

Multiply $5$ by $- 1$ .

$f (- 1) = 1 - 2 - 5 + 6$

Simplify by adding and subtracting.

Subtract $2$ from $1$ .

$f (- 1) = - 1 - 5 + 6$

Subtract $5$ from $- 1$ .

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

Add $- 6$ and $6$ .

$f (- 1) = 0$

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.

$f (0) = - {(0)}^{3} - 2 {(0)}^{2} + 5 (0) + 6$

Simplify the result.

Simplify each term.

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

$f (0) = - 0 - 2 {(0)}^{2} + 5 (0) + 6$

Multiply $- 1$ by $0$ .

$f (0) = 0 - 2 {(0)}^{2} + 5 (0) + 6$

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

$f (0) = 0 - 2 \cdot 0 + 5 (0) + 6$

Multiply $- 2$ by $0$ .

$f (0) = 0 + 0 + 5 (0) + 6$

Multiply $5$ by $0$ .

$f (0) = 0 + 0 + 0 + 6$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0 + 6$

Add $0$ and $0$ .

$f (0) = 0 + 6$

Add $0$ and $6$ .

$f (0) = 6$

The final answer is $6$ .

$6$

Convert $6$ to decimal.

$y = 6$

Find the point at $x = 1$ .

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

$f (1) = - {(1)}^{3} - 2 {(1)}^{2} + 5 (1) + 6$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = - 1 \cdot 1 - 2 {(1)}^{2} + 5 (1) + 6$

Multiply $- 1$ by $1$ .

$f (1) = - 1 - 2 {(1)}^{2} + 5 (1) + 6$

One to any power is one.

$f (1) = - 1 - 2 \cdot 1 + 5 (1) + 6$

Multiply $- 2$ by $1$ .

$f (1) = - 1 - 2 + 5 (1) + 6$

Multiply $5$ by $1$ .

$f (1) = - 1 - 2 + 5 + 6$

Simplify by adding and subtracting.

Subtract $2$ from $- 1$ .

$f (1) = - 3 + 5 + 6$

Add $- 3$ and $5$ .

$f (1) = 2 + 6$

Add $2$ and $6$ .

$f (1) = 8$

The final answer is $8$ .

$8$

Convert $8$ to decimal.

$y = 8$

Find the point at $x = 2$ .

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

$f (2) = - {(2)}^{3} - 2 {(2)}^{2} + 5 (2) + 6$

Simplify the result.

Simplify each term.

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

$f (2) = - 1 \cdot 8 - 2 {(2)}^{2} + 5 (2) + 6$

Multiply $- 1$ by $8$ .

$f (2) = - 8 - 2 {(2)}^{2} + 5 (2) + 6$

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

$f (2) = - 8 - 2 \cdot 4 + 5 (2) + 6$

Multiply $- 2$ by $4$ .

$f (2) = - 8 - 8 + 5 (2) + 6$

Multiply $5$ by $2$ .

$f (2) = - 8 - 8 + 10 + 6$

Simplify by adding and subtracting.

Subtract $8$ from $- 8$ .

$f (2) = - 16 + 10 + 6$

Add $- 16$ and $10$ .

$f (2) = - 6 + 6$

Add $- 6$ and $6$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

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

$\begin{array}{c} x & y \\ - 2 & - 4 \\ - 1 & 0 \\ 0 & 6 \\ 1 & 8 \\ 2 & 0 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 2 & - 4 \\ - 1 & 0 \\ 0 & 6 \\ 1 & 8 \\ 2 & 0 \end{array}$

Graph -(x+3)(x+1)(x-2)

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