Graph f(x)=(x+1)(x^2+2)

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

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $2$ by $- 2$ .

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

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

$f (- 2) = - 8 - 4 + 4 + 2$

Simplify by adding and subtracting.

Subtract $4$ from $- 8$ .

$f (- 2) = - 12 + 4 + 2$

Add $- 12$ and $4$ .

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

Add $- 8$ and $2$ .

$f (- 2) = - 6$

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.

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

Simplify the result.

Simplify each term.

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

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

Multiply $2$ by $- 1$ .

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

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

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

Simplify by adding and subtracting.

Subtract $2$ from $- 1$ .

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

Add $- 3$ and $1$ .

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

Add $- 2$ and $2$ .

$f (- 1) = 0$

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.

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

Simplify the result.

Simplify each term.

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

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

Multiply $2$ by $0$ .

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

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

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

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.

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

Simplify the result.

Simplify each term.

One to any power is one.

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

Multiply $2$ by $1$ .

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

One to any power is one.

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

Simplify by adding numbers.

Add $1$ and $2$ .

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

Add $3$ and $1$ .

$f (1) = 4 + 2$

Add $4$ and $2$ .

$f (1) = 6$

The final answer is $6$ .

$6$

Convert $6$ to decimal.

$y = 6$

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

$f (2) = 8 + 2 (2) + {(2)}^{2} + 2$

Multiply $2$ by $2$ .

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

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

$f (2) = 8 + 4 + 4 + 2$

Simplify by adding numbers.

Add $8$ and $4$ .

$f (2) = 12 + 4 + 2$

Add $12$ and $4$ .

$f (2) = 16 + 2$

Add $16$ and $2$ .

$f (2) = 18$

The final answer is $18$ .

$18$

Convert $18$ to decimal.

$y = 18$

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

$\begin{array}{c} x & y \\ - 2 & - 6 \\ - 1 & 0 \\ 0 & 2 \\ 1 & 6 \\ 2 & 18 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 2 & - 6 \\ - 1 & 0 \\ 0 & 2 \\ 1 & 6 \\ 2 & 18 \end{array}$

Graph f(x)=(x+1)(x^2+2)

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