Graph f(x)=-3(x+1)(x^2-4)

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

Step 1

Find the point at $x = - 2$ .

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

$f (- 2) = - 3 {(- 2)}^{3} + 12 (- 2) - 3 {(- 2)}^{2} + 12$

Simplify the result.

Simplify each term.

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

$f (- 2) = - 3 \cdot - 8 + 12 (- 2) - 3 {(- 2)}^{2} + 12$

Multiply $- 3$ by $- 8$ .

$f (- 2) = 24 + 12 (- 2) - 3 {(- 2)}^{2} + 12$

Multiply $12$ by $- 2$ .

$f (- 2) = 24 - 24 - 3 {(- 2)}^{2} + 12$

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

$f (- 2) = 24 - 24 - 3 \cdot 4 + 12$

Multiply $- 3$ by $4$ .

$f (- 2) = 24 - 24 - 12 + 12$

Simplify by adding and subtracting.

Subtract $24$ from $24$ .

$f (- 2) = 0 - 12 + 12$

Subtract $12$ from $0$ .

$f (- 2) = - 12 + 12$

Add $- 12$ and $12$ .

$f (- 2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 2

Find the point at $x = 0$ .

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

$f (0) = - 3 {(0)}^{3} + 12 (0) - 3 {(0)}^{2} + 12$

Simplify the result.

Simplify each term.

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

$f (0) = - 3 \cdot 0 + 12 (0) - 3 {(0)}^{2} + 12$

Multiply $- 3$ by $0$ .

$f (0) = 0 + 12 (0) - 3 {(0)}^{2} + 12$

Multiply $12$ by $0$ .

$f (0) = 0 + 0 - 3 {(0)}^{2} + 12$

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

$f (0) = 0 + 0 - 3 \cdot 0 + 12$

Multiply $- 3$ by $0$ .

$f (0) = 0 + 0 + 0 + 12$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0 + 12$

Add $0$ and $0$ .

$f (0) = 0 + 12$

Add $0$ and $12$ .

$f (0) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

Step 3

Find the point at $x = 1$ .

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

$f (1) = - 3 {(1)}^{3} + 12 (1) - 3 {(1)}^{2} + 12$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = - 3 \cdot 1 + 12 (1) - 3 {(1)}^{2} + 12$

Multiply $- 3$ by $1$ .

$f (1) = - 3 + 12 (1) - 3 {(1)}^{2} + 12$

Multiply $12$ by $1$ .

$f (1) = - 3 + 12 - 3 {(1)}^{2} + 12$

One to any power is one.

$f (1) = - 3 + 12 - 3 \cdot 1 + 12$

Multiply $- 3$ by $1$ .

$f (1) = - 3 + 12 - 3 + 12$

Simplify by adding and subtracting.

Add $- 3$ and $12$ .

$f (1) = 9 - 3 + 12$

Subtract $3$ from $9$ .

$f (1) = 6 + 12$

Add $6$ and $12$ .

$f (1) = 18$

The final answer is $18$ .

$18$

Convert $18$ to decimal.

$y = 18$

Step 4

Find the point at $x = 2$ .

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

$f (2) = - 3 {(2)}^{3} + 12 (2) - 3 {(2)}^{2} + 12$

Simplify the result.

Simplify each term.

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

$f (2) = - 3 \cdot 8 + 12 (2) - 3 {(2)}^{2} + 12$

Multiply $- 3$ by $8$ .

$f (2) = - 24 + 12 (2) - 3 {(2)}^{2} + 12$

Multiply $12$ by $2$ .

$f (2) = - 24 + 24 - 3 {(2)}^{2} + 12$

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

$f (2) = - 24 + 24 - 3 \cdot 4 + 12$

Multiply $- 3$ by $4$ .

$f (2) = - 24 + 24 - 12 + 12$

Simplify by adding and subtracting.

Add $- 24$ and $24$ .

$f (2) = 0 - 12 + 12$

Subtract $12$ from $0$ .

$f (2) = - 12 + 12$

Add $- 12$ and $12$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 5

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

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & 0 \\ 0 & 12 \\ 1 & 18 \\ 2 & 0 \end{array}$

Step 6

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & 0 \\ 0 & 12 \\ 1 & 18 \\ 2 & 0 \end{array}$

Step 7

Graph f(x)=-3(x+1)(x^2-4)

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