Graph y=(x+4)^2(x+1)

$y = {(x + 4)}^{2} (x + 1)$

Find the point at $x = - 5$ .

Replace the variable $x$ with $- 5$ in the expression.

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

Simplify the result.

Simplify each term.

Add $- 5$ and $4$ .

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

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

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

Multiply $- 5$ by $1$ .

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

Add $- 5$ and $4$ .

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

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

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

Add $- 5$ and $1$ .

$f (- 5) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Find the point at $x = - 4$ .

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

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

Simplify the result.

Simplify each term.

Add $- 4$ and $4$ .

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

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

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

Multiply $- 4$ by $0$ .

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

Add $- 4$ and $4$ .

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

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

$f (- 4) = 0 + 0$

Add $0$ and $0$ .

$f (- 4) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = - 3$ .

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

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

Simplify the result.

Simplify each term.

Add $- 3$ and $4$ .

$f (- 3) = - 3 \cdot 1^{2} + {((- 3) + 4)}^{2}$

One to any power is one.

$f (- 3) = - 3 \cdot 1 + {((- 3) + 4)}^{2}$

Multiply $- 3$ by $1$ .

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

Add $- 3$ and $4$ .

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

One to any power is one.

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

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.

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

Simplify the result.

Simplify each term.

Add $- 2$ and $4$ .

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

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

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

Multiply $- 2$ by $4$ .

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

Add $- 2$ and $4$ .

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

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

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

Add $- 8$ and $4$ .

$f (- 2) = - 4$

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.

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

Simplify the result.

Simplify each term.

Add $- 1$ and $4$ .

$f (- 1) = - 1 \cdot 3^{2} + {((- 1) + 4)}^{2}$

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

$f (- 1) = - 1 \cdot 9 + {((- 1) + 4)}^{2}$

Multiply $- 1$ by $9$ .

$f (- 1) = - 9 + {((- 1) + 4)}^{2}$

Add $- 1$ and $4$ .

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

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

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

Add $- 9$ and $9$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

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

$\begin{array}{c} x & y \\ - 5 & - 4 \\ - 4 & 0 \\ - 3 & - 2 \\ - 2 & - 4 \\ - 1 & 0 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 5 & - 4 \\ - 4 & 0 \\ - 3 & - 2 \\ - 2 & - 4 \\ - 1 & 0 \end{array}$

Graph y=(x+4)^2(x+1)

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