Algebra Examples

$p (x) = (x + 5) (x + 2) (x)$

Step 1

Find the point at $x = - 4$ .

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Step 1.1

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

$f (- 4) = {(- 4)}^{3} + 7 {(- 4)}^{2} + 10 (- 4)$

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

Raise $- 4$ to the power of $3$ .

$f (- 4) = - 64 + 7 {(- 4)}^{2} + 10 (- 4)$

Step 1.2.1.2

Raise $- 4$ to the power of $2$ .

$f (- 4) = - 64 + 7 \cdot 16 + 10 (- 4)$

Step 1.2.1.3

Multiply $7$ by $16$ .

$f (- 4) = - 64 + 112 + 10 (- 4)$

Step 1.2.1.4

Multiply $10$ by $- 4$ .

$f (- 4) = - 64 + 112 - 40$

Step 1.2.2

Simplify by adding and subtracting.

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Step 1.2.2.1

Add $- 64$ and $112$ .

$f (- 4) = 48 - 40$

Step 1.2.2.2

Subtract $40$ from $48$ .

$f (- 4) = 8$

Step 1.2.3

The final answer is $8$ .

$8$

Step 1.3

Convert $8$ to decimal.

$y = 8$

Step 2

Find the point at $x = - 3$ .

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Step 2.1

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

$f (- 3) = {(- 3)}^{3} + 7 {(- 3)}^{2} + 10 (- 3)$

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

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

$f (- 3) = - 27 + 7 {(- 3)}^{2} + 10 (- 3)$

Step 2.2.1.2

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

$f (- 3) = - 27 + 7 \cdot 9 + 10 (- 3)$

Step 2.2.1.3

Multiply $7$ by $9$ .

$f (- 3) = - 27 + 63 + 10 (- 3)$

Step 2.2.1.4

Multiply $10$ by $- 3$ .

$f (- 3) = - 27 + 63 - 30$

Step 2.2.2

Simplify by adding and subtracting.

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Step 2.2.2.1

Add $- 27$ and $63$ .

$f (- 3) = 36 - 30$

Step 2.2.2.2

Subtract $30$ from $36$ .

$f (- 3) = 6$

Step 2.2.3

The final answer is $6$ .

$6$

Step 2.3

Convert $6$ to decimal.

$y = 6$

Step 3

Find the point at $x = - 2$ .

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Step 3.1

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

$f (- 2) = {(- 2)}^{3} + 7 {(- 2)}^{2} + 10 (- 2)$

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

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

$f (- 2) = - 8 + 7 {(- 2)}^{2} + 10 (- 2)$

Step 3.2.1.2

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

$f (- 2) = - 8 + 7 \cdot 4 + 10 (- 2)$

Step 3.2.1.3

Multiply $7$ by $4$ .

$f (- 2) = - 8 + 28 + 10 (- 2)$

Step 3.2.1.4

Multiply $10$ by $- 2$ .

$f (- 2) = - 8 + 28 - 20$

Step 3.2.2

Simplify by adding and subtracting.

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Step 3.2.2.1

Add $- 8$ and $28$ .

$f (- 2) = 20 - 20$

Step 3.2.2.2

Subtract $20$ from $20$ .

$f (- 2) = 0$

Step 3.2.3

The final answer is $0$ .

$0$

Step 3.3

Convert $0$ to decimal.

$y = 0$

Step 4

Find the point at $x = - 1$ .

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Step 4.1

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

$f (- 1) = {(- 1)}^{3} + 7 {(- 1)}^{2} + 10 (- 1)$

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

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

$f (- 1) = - 1 + 7 {(- 1)}^{2} + 10 (- 1)$

Step 4.2.1.2

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

$f (- 1) = - 1 + 7 \cdot 1 + 10 (- 1)$

Step 4.2.1.3

Multiply $7$ by $1$ .

$f (- 1) = - 1 + 7 + 10 (- 1)$

Step 4.2.1.4

Multiply $10$ by $- 1$ .

$f (- 1) = - 1 + 7 - 10$

Step 4.2.2

Simplify by adding and subtracting.

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Step 4.2.2.1

Add $- 1$ and $7$ .

$f (- 1) = 6 - 10$

Step 4.2.2.2

Subtract $10$ from $6$ .

$f (- 1) = - 4$

Step 4.2.3

The final answer is $- 4$ .

$- 4$

Step 4.3

Convert $- 4$ to decimal.

$y = - 4$

Step 5

Find the point at $x = 0$ .

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Step 5.1

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

$f (0) = {(0)}^{3} + 7 {(0)}^{2} + 10 (0)$

Step 5.2

Simplify the result.

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

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

$f (0) = 0 + 7 {(0)}^{2} + 10 (0)$

Step 5.2.1.2

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

$f (0) = 0 + 7 \cdot 0 + 10 (0)$

Step 5.2.1.3

Multiply $7$ by $0$ .

$f (0) = 0 + 0 + 10 (0)$

Step 5.2.1.4

Multiply $10$ by $0$ .

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

Step 5.2.2

Simplify by adding numbers.

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Step 5.2.2.1

Add $0$ and $0$ .

$f (0) = 0 + 0$

Step 5.2.2.2

Add $0$ and $0$ .

$f (0) = 0$

Step 5.2.3

The final answer is $0$ .

$0$

Step 5.3

Convert $0$ to decimal.

$y = 0$

Step 6

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

$\begin{array}{c} x & y \\ - 4 & 8 \\ - 3 & 6 \\ - 2 & 0 \\ - 1 & - 4 \\ 0 & 0 \end{array}$

Step 7

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 4 & 8 \\ - 3 & 6 \\ - 2 & 0 \\ - 1 & - 4 \\ 0 & 0 \end{array}$

Step 8