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

$y = (x + 1) (x^{2} + 3 x + 2)$

Find the point at $x = - 3$ .

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

$f (- 3) = {(- 3)}^{3} + 4 {(- 3)}^{2} + 5 (- 3) + 2$

Simplify the result.

Simplify each term.

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

$f (- 3) = - 27 + 4 {(- 3)}^{2} + 5 (- 3) + 2$

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

$f (- 3) = - 27 + 4 \cdot 9 + 5 (- 3) + 2$

Multiply $4$ by $9$ .

$f (- 3) = - 27 + 36 + 5 (- 3) + 2$

Multiply $5$ by $- 3$ .

$f (- 3) = - 27 + 36 - 15 + 2$

Simplify by adding and subtracting.

Add $- 27$ and $36$ .

$f (- 3) = 9 - 15 + 2$

Subtract $15$ from $9$ .

$f (- 3) = - 6 + 2$

Add $- 6$ and $2$ .

$f (- 3) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Find the point at $x = - 2$ .

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

$f (- 2) = {(- 2)}^{3} + 4 {(- 2)}^{2} + 5 (- 2) + 2$

Simplify the result.

Simplify each term.

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

$f (- 2) = - 8 + 4 {(- 2)}^{2} + 5 (- 2) + 2$

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

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

Multiply $4$ by $4$ .

$f (- 2) = - 8 + 16 + 5 (- 2) + 2$

Multiply $5$ by $- 2$ .

$f (- 2) = - 8 + 16 - 10 + 2$

Simplify by adding and subtracting.

Add $- 8$ and $16$ .

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

Subtract $10$ from $8$ .

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

Add $- 2$ and $2$ .

$f (- 2) = 0$

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.

$f (0) = {(0)}^{3} + 4 {(0)}^{2} + 5 (0) + 2$

Simplify the result.

Simplify each term.

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

$f (0) = 0 + 4 {(0)}^{2} + 5 (0) + 2$

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

$f (0) = 0 + 4 \cdot 0 + 5 (0) + 2$

Multiply $4$ by $0$ .

$f (0) = 0 + 0 + 5 (0) + 2$

Multiply $5$ by $0$ .

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

Simplify by adding numbers.

Add $0$ and $0$ .

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

Add $0$ and $0$ .

$f (0) = 0 + 2$

Add $0$ and $2$ .

$f (0) = 2$

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.

$f (1) = {(1)}^{3} + 4 {(1)}^{2} + 5 (1) + 2$

Simplify the result.

Simplify each term.

One to any power is one.

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

One to any power is one.

$f (1) = 1 + 4 \cdot 1 + 5 (1) + 2$

Multiply $4$ by $1$ .

$f (1) = 1 + 4 + 5 (1) + 2$

Multiply $5$ by $1$ .

$f (1) = 1 + 4 + 5 + 2$

Simplify by adding numbers.

Add $1$ and $4$ .

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

Add $5$ and $5$ .

$f (1) = 10 + 2$

Add $10$ and $2$ .

$f (1) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

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

$\begin{array}{c} x & y \\ - 3 & - 4 \\ - 2 & 0 \\ - 1 & 0 \\ 0 & 2 \\ 1 & 12 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 3 & - 4 \\ - 2 & 0 \\ - 1 & 0 \\ 0 & 2 \\ 1 & 12 \end{array}$

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

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