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

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

Find the point at $x = - 3$ .

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

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

Simplify the result.

Simplify each term.

Add $- 3$ and $2$ .

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

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

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

Multiply $- 3$ by $1$ .

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

Add $- 3$ and $2$ .

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

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

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

Add $- 3$ and $1$ .

$f (- 3) = - 2$

The final answer is $- 2$ .

$- 2$

Convert $- 2$ to decimal.

$y = - 2$

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

Add $- 2$ and $2$ .

$f (- 2) = - 2 \cdot 0^{2} + {((- 2) + 2)}^{2}$

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

$f (- 2) = - 2 \cdot 0 + {((- 2) + 2)}^{2}$

Multiply $- 2$ by $0$ .

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

Add $- 2$ and $2$ .

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

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

$f (- 2) = 0 + 0$

Add $0$ and $0$ .

$f (- 2) = 0$

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.

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

Simplify the result.

Simplify each term.

Add $0$ and $2$ .

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

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

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

Multiply $0$ by $4$ .

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

Add $0$ and $2$ .

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

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

$f (0) = 0 + 4$

Add $0$ and $4$ .

$f (0) = 4$

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.

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

Simplify the result.

Simplify each term.

Multiply ${((1) + 2)}^{2}$ by $1$ .

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

Add $1$ and $2$ .

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

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

$f (1) = 9 + {((1) + 2)}^{2}$

Add $1$ and $2$ .

$f (1) = 9 + 3^{2}$

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

$f (1) = 9 + 9$

Add $9$ and $9$ .

$f (1) = 18$

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.

$\begin{array}{c} x & y \\ - 3 & - 2 \\ - 2 & 0 \\ - 1 & 0 \\ 0 & 4 \\ 1 & 18 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 3 & - 2 \\ - 2 & 0 \\ - 1 & 0 \\ 0 & 4 \\ 1 & 18 \end{array}$

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

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