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

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

Find the point at $x = - 3$ .

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

$f (- 3) = 2 {(- 3)}^{3} + 11 {(- 3)}^{2} + 17 (- 3) + 6$

Simplify the result.

Simplify each term.

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

$f (- 3) = 2 \cdot - 27 + 11 {(- 3)}^{2} + 17 (- 3) + 6$

Multiply $2$ by $- 27$ .

$f (- 3) = - 54 + 11 {(- 3)}^{2} + 17 (- 3) + 6$

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

$f (- 3) = - 54 + 11 \cdot 9 + 17 (- 3) + 6$

Multiply $11$ by $9$ .

$f (- 3) = - 54 + 99 + 17 (- 3) + 6$

Multiply $17$ by $- 3$ .

$f (- 3) = - 54 + 99 - 51 + 6$

Simplify by adding and subtracting.

Add $- 54$ and $99$ .

$f (- 3) = 45 - 51 + 6$

Subtract $51$ from $45$ .

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

Add $- 6$ and $6$ .

$f (- 3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = - 1$ .

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

$f (- 1) = 2 {(- 1)}^{3} + 11 {(- 1)}^{2} + 17 (- 1) + 6$

Simplify the result.

Simplify each term.

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

$f (- 1) = 2 \cdot - 1 + 11 {(- 1)}^{2} + 17 (- 1) + 6$

Multiply $2$ by $- 1$ .

$f (- 1) = - 2 + 11 {(- 1)}^{2} + 17 (- 1) + 6$

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

$f (- 1) = - 2 + 11 \cdot 1 + 17 (- 1) + 6$

Multiply $11$ by $1$ .

$f (- 1) = - 2 + 11 + 17 (- 1) + 6$

Multiply $17$ by $- 1$ .

$f (- 1) = - 2 + 11 - 17 + 6$

Simplify by adding and subtracting.

Add $- 2$ and $11$ .

$f (- 1) = 9 - 17 + 6$

Subtract $17$ from $9$ .

$f (- 1) = - 8 + 6$

Add $- 8$ and $6$ .

$f (- 1) = - 2$

The final answer is $- 2$ .

$- 2$

Convert $- 2$ to decimal.

$y = - 2$

Find the point at $x = 0$ .

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

$f (0) = 2 {(0)}^{3} + 11 {(0)}^{2} + 17 (0) + 6$

Simplify the result.

Simplify each term.

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

$f (0) = 2 \cdot 0 + 11 {(0)}^{2} + 17 (0) + 6$

Multiply $2$ by $0$ .

$f (0) = 0 + 11 {(0)}^{2} + 17 (0) + 6$

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

$f (0) = 0 + 11 \cdot 0 + 17 (0) + 6$

Multiply $11$ by $0$ .

$f (0) = 0 + 0 + 17 (0) + 6$

Multiply $17$ 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.

$f (1) = 2 {(1)}^{3} + 11 {(1)}^{2} + 17 (1) + 6$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 2 \cdot 1 + 11 {(1)}^{2} + 17 (1) + 6$

Multiply $2$ by $1$ .

$f (1) = 2 + 11 {(1)}^{2} + 17 (1) + 6$

One to any power is one.

$f (1) = 2 + 11 \cdot 1 + 17 (1) + 6$

Multiply $11$ by $1$ .

$f (1) = 2 + 11 + 17 (1) + 6$

Multiply $17$ by $1$ .

$f (1) = 2 + 11 + 17 + 6$

Simplify by adding numbers.

Add $2$ and $11$ .

$f (1) = 13 + 17 + 6$

Add $13$ and $17$ .

$f (1) = 30 + 6$

Add $30$ and $6$ .

$f (1) = 36$

The final answer is $36$ .

$36$

Convert $36$ to decimal.

$y = 36$

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

$\begin{array}{c} x & y \\ - 3 & 0 \\ - 2 & 0 \\ - 1 & - 2 \\ 0 & 6 \\ 1 & 36 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 3 & 0 \\ - 2 & 0 \\ - 1 & - 2 \\ 0 & 6 \\ 1 & 36 \end{array}$

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

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