Graph f(x)=2(x+1)(x^2-9)

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

Step 1

Find the point at $x = - 2$ .

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

$f (- 2) = 2 {(- 2)}^{3} - 18 \cdot - 2 + 2 {(- 2)}^{2} - 18$

Simplify the result.

Simplify each term.

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

$f (- 2) = 2 \cdot - 8 - 18 \cdot - 2 + 2 {(- 2)}^{2} - 18$

Multiply $2$ by $- 8$ .

$f (- 2) = - 16 - 18 \cdot - 2 + 2 {(- 2)}^{2} - 18$

Multiply $- 18$ by $- 2$ .

$f (- 2) = - 16 + 36 + 2 {(- 2)}^{2} - 18$

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

$f (- 2) = - 16 + 36 + 2 \cdot 4 - 18$

Multiply $2$ by $4$ .

$f (- 2) = - 16 + 36 + 8 - 18$

Simplify by adding and subtracting.

Add $- 16$ and $36$ .

$f (- 2) = 20 + 8 - 18$

Add $20$ and $8$ .

$f (- 2) = 28 - 18$

Subtract $18$ from $28$ .

$f (- 2) = 10$

The final answer is $10$ .

$10$

Convert $10$ to decimal.

$y = 10$

Step 2

Find the point at $x = - 1$ .

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

$f (- 1) = 2 {(- 1)}^{3} - 18 \cdot - 1 + 2 {(- 1)}^{2} - 18$

Simplify the result.

Simplify each term.

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

$f (- 1) = 2 \cdot - 1 - 18 \cdot - 1 + 2 {(- 1)}^{2} - 18$

Multiply $2$ by $- 1$ .

$f (- 1) = - 2 - 18 \cdot - 1 + 2 {(- 1)}^{2} - 18$

Multiply $- 18$ by $- 1$ .

$f (- 1) = - 2 + 18 + 2 {(- 1)}^{2} - 18$

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

$f (- 1) = - 2 + 18 + 2 \cdot 1 - 18$

Multiply $2$ by $1$ .

$f (- 1) = - 2 + 18 + 2 - 18$

Simplify by adding and subtracting.

Add $- 2$ and $18$ .

$f (- 1) = 16 + 2 - 18$

Add $16$ and $2$ .

$f (- 1) = 18 - 18$

Subtract $18$ from $18$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 0$ .

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

$f (0) = 2 {(0)}^{3} - 18 \cdot 0 + 2 {(0)}^{2} - 18$

Simplify the result.

Simplify each term.

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

$f (0) = 2 \cdot 0 - 18 \cdot 0 + 2 {(0)}^{2} - 18$

Multiply $2$ by $0$ .

$f (0) = 0 - 18 \cdot 0 + 2 {(0)}^{2} - 18$

Multiply $- 18$ by $0$ .

$f (0) = 0 + 0 + 2 {(0)}^{2} - 18$

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

$f (0) = 0 + 0 + 2 \cdot 0 - 18$

Multiply $2$ by $0$ .

$f (0) = 0 + 0 + 0 - 18$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$f (0) = 0 + 0 - 18$

Add $0$ and $0$ .

$f (0) = 0 - 18$

Subtract $18$ from $0$ .

$f (0) = - 18$

The final answer is $- 18$ .

$- 18$

Convert $- 18$ to decimal.

$y = - 18$

Step 4

Find the point at $x = 1$ .

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

$f (1) = 2 {(1)}^{3} - 18 \cdot 1 + 2 {(1)}^{2} - 18$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 2 \cdot 1 - 18 \cdot 1 + 2 {(1)}^{2} - 18$

Multiply $2$ by $1$ .

$f (1) = 2 - 18 \cdot 1 + 2 {(1)}^{2} - 18$

Multiply $- 18$ by $1$ .

$f (1) = 2 - 18 + 2 {(1)}^{2} - 18$

One to any power is one.

$f (1) = 2 - 18 + 2 \cdot 1 - 18$

Multiply $2$ by $1$ .

$f (1) = 2 - 18 + 2 - 18$

Simplify by adding and subtracting.

Subtract $18$ from $2$ .

$f (1) = - 16 + 2 - 18$

Add $- 16$ and $2$ .

$f (1) = - 14 - 18$

Subtract $18$ from $- 14$ .

$f (1) = - 32$

The final answer is $- 32$ .

$- 32$

Convert $- 32$ to decimal.

$y = - 32$

Step 5

Find the point at $x = 2$ .

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

$f (2) = 2 {(2)}^{3} - 18 \cdot 2 + 2 {(2)}^{2} - 18$

Simplify the result.

Simplify each term.

Multiply $2$ by ${(2)}^{3}$ by adding the exponents.

Multiply $2$ by ${(2)}^{3}$ .

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

$f (2) = 2 {(2)}^{3} - 18 \cdot 2 + 2 {(2)}^{2} - 18$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (2) = 2^{1 + 3} - 18 \cdot 2 + 2 {(2)}^{2} - 18$

Add $1$ and $3$ .

$f (2) = 2^{4} - 18 \cdot 2 + 2 {(2)}^{2} - 18$

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

$f (2) = 16 - 18 \cdot 2 + 2 {(2)}^{2} - 18$

Multiply $- 18$ by $2$ .

$f (2) = 16 - 36 + 2 {(2)}^{2} - 18$

Multiply $2$ by ${(2)}^{2}$ by adding the exponents.

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

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

$f (2) = 16 - 36 + 2 {(2)}^{2} - 18$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (2) = 16 - 36 + 2^{1 + 2} - 18$

Add $1$ and $2$ .

$f (2) = 16 - 36 + 2^{3} - 18$

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

$f (2) = 16 - 36 + 8 - 18$

Simplify by adding and subtracting.

Subtract $36$ from $16$ .

$f (2) = - 20 + 8 - 18$

Add $- 20$ and $8$ .

$f (2) = - 12 - 18$

Subtract $18$ from $- 12$ .

$f (2) = - 30$

The final answer is $- 30$ .

$- 30$

Convert $- 30$ to decimal.

$y = - 30$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & 10 \\ - 1 & 0 \\ 0 & - 18 \\ 1 & - 32 \\ 2 & - 30 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & 10 \\ - 1 & 0 \\ 0 & - 18 \\ 1 & - 32 \\ 2 & - 30 \end{array}$

Step 8

Graph f(x)=2(x+1)(x^2-9)

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