Algebra Examples

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

Step 1

Find the point at $x = - 3$ .

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Step 1.1

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

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

Step 1.2

Simplify the result.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Add $- 3$ and $2$ .

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

Step 1.2.1.2

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

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

Step 1.2.1.3

Multiply $- 3$ by $1$ .

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

Step 1.2.1.4

Add $- 3$ and $2$ .

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

Step 1.2.1.5

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

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

Step 1.2.2

Add $- 3$ and $1$ .

$f (- 3) = - 2$

Step 1.2.3

The final answer is $- 2$ .

$- 2$

Step 1.3

Convert $- 2$ to decimal.

$y = - 2$

Step 2

Find the point at $x = - 2$ .

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Step 2.1

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

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

Step 2.2

Simplify the result.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Add $- 2$ and $2$ .

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

Step 2.2.1.2

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

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

Step 2.2.1.3

Multiply $- 2$ by $0$ .

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

Step 2.2.1.4

Add $- 2$ and $2$ .

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

Step 2.2.1.5

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

$f (- 2) = 0 + 0$

Step 2.2.2

Add $0$ and $0$ .

$f (- 2) = 0$

Step 2.2.3

The final answer is $0$ .

$0$

Step 2.3

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 0$ .

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Step 3.1

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

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

Step 3.2

Simplify the result.

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Add $0$ and $2$ .

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

Step 3.2.1.2

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

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

Step 3.2.1.3

Multiply $0$ by $4$ .

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

Step 3.2.1.4

Add $0$ and $2$ .

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

Step 3.2.1.5

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

$f (0) = 0 + 4$

Step 3.2.2

Add $0$ and $4$ .

$f (0) = 4$

Step 3.2.3

The final answer is $4$ .

$4$

Step 3.3

Convert $4$ to decimal.

$y = 4$

Step 4

Find the point at $x = 1$ .

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Step 4.1

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

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

Step 4.2

Simplify the result.

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

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

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

Step 4.2.1.2

Add $1$ and $2$ .

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

Step 4.2.1.3

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

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

Step 4.2.1.4

Add $1$ and $2$ .

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

Step 4.2.1.5

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

$f (1) = 9 + 9$

Step 4.2.2

Add $9$ and $9$ .

$f (1) = 18$

Step 4.2.3

The final answer is $18$ .

$18$

Step 4.3

Convert $18$ to decimal.

$y = 18$

Step 5

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

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

Step 6

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

Falls to the left and rises to the right

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

Step 7