Graph P(x)=(x+3)(x+2)(x+1)

$P (x) = (x + 3) (x + 2) (x + 1)$

Find the point at $x = - 4$ .

Replace the variable $x$ with $- 4$ in the expression.

$f (- 4) = {(- 4)}^{3} + 6 {(- 4)}^{2} + 11 (- 4) + 6$

Simplify the result.

Simplify each term.

Raise $- 4$ to the power of $3$ .

$f (- 4) = - 64 + 6 {(- 4)}^{2} + 11 (- 4) + 6$

Raise $- 4$ to the power of $2$ .

$f (- 4) = - 64 + 6 \cdot 16 + 11 (- 4) + 6$

Multiply $6$ by $16$ .

$f (- 4) = - 64 + 96 + 11 (- 4) + 6$

Multiply $11$ by $- 4$ .

$f (- 4) = - 64 + 96 - 44 + 6$

Simplify by adding and subtracting.

Add $- 64$ and $96$ .

$f (- 4) = 32 - 44 + 6$

Subtract $44$ from $32$ .

$f (- 4) = - 12 + 6$

Add $- 12$ and $6$ .

$f (- 4) = - 6$

The final answer is $- 6$ .

$- 6$

Convert $- 6$ to decimal.

$y = - 6$

Find the point at $x = - 3$ .

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

$f (- 3) = {(- 3)}^{3} + 6 {(- 3)}^{2} + 11 (- 3) + 6$

Simplify the result.

Simplify each term.

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

$f (- 3) = - 27 + 6 {(- 3)}^{2} + 11 (- 3) + 6$

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

$f (- 3) = - 27 + 6 \cdot 9 + 11 (- 3) + 6$

Multiply $6$ by $9$ .

$f (- 3) = - 27 + 54 + 11 (- 3) + 6$

Multiply $11$ by $- 3$ .

$f (- 3) = - 27 + 54 - 33 + 6$

Simplify by adding and subtracting.

Add $- 27$ and $54$ .

$f (- 3) = 27 - 33 + 6$

Subtract $33$ from $27$ .

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

Add $- 6$ and $6$ .

$f (- 3) = 0$

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.

$f (0) = {(0)}^{3} + 6 {(0)}^{2} + 11 (0) + 6$

Simplify the result.

Simplify each term.

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

$f (0) = 0 + 6 {(0)}^{2} + 11 (0) + 6$

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

$f (0) = 0 + 6 \cdot 0 + 11 (0) + 6$

Multiply $6$ by $0$ .

$f (0) = 0 + 0 + 11 (0) + 6$

Multiply $11$ 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.

$y = 6$

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

$\begin{array}{c} x & y \\ - 4 & - 6 \\ - 3 & 0 \\ - 2 & 0 \\ - 1 & 0 \\ 0 & 6 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 4 & - 6 \\ - 3 & 0 \\ - 2 & 0 \\ - 1 & 0 \\ 0 & 6 \end{array}$

Graph P(x)=(x+3)(x+2)(x+1)

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