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

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

Step 1

Find the point at $x = 0$ .

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

$f (0) = - 2 {(0)}^{3} + 2 (0) + 8 {(0)}^{2} - 8$

Simplify the result.

Simplify each term.

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

$f (0) = - 2 \cdot 0 + 2 (0) + 8 {(0)}^{2} - 8$

Multiply $- 2$ by $0$ .

$f (0) = 0 + 2 (0) + 8 {(0)}^{2} - 8$

Multiply $2$ by $0$ .

$f (0) = 0 + 0 + 8 {(0)}^{2} - 8$

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

$f (0) = 0 + 0 + 8 \cdot 0 - 8$

Multiply $8$ by $0$ .

$f (0) = 0 + 0 + 0 - 8$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$f (0) = 0 + 0 - 8$

Add $0$ and $0$ .

$f (0) = 0 - 8$

Subtract $8$ from $0$ .

$f (0) = - 8$

The final answer is $- 8$ .

$- 8$

Convert $- 8$ to decimal.

$y = - 8$

Step 2

Find the point at $x = 1$ .

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

$f (1) = - 2 {(1)}^{3} + 2 (1) + 8 {(1)}^{2} - 8$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = - 2 \cdot 1 + 2 (1) + 8 {(1)}^{2} - 8$

Multiply $- 2$ by $1$ .

$f (1) = - 2 + 2 (1) + 8 {(1)}^{2} - 8$

Multiply $2$ by $1$ .

$f (1) = - 2 + 2 + 8 {(1)}^{2} - 8$

One to any power is one.

$f (1) = - 2 + 2 + 8 \cdot 1 - 8$

Multiply $8$ by $1$ .

$f (1) = - 2 + 2 + 8 - 8$

Simplify by adding and subtracting.

Add $- 2$ and $2$ .

$f (1) = 0 + 8 - 8$

Add $0$ and $8$ .

$f (1) = 8 - 8$

Subtract $8$ from $8$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 2$ by $8$ .

$f (2) = - 16 + 2 (2) + 8 {(2)}^{2} - 8$

Multiply $2$ by $2$ .

$f (2) = - 16 + 4 + 8 {(2)}^{2} - 8$

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

$f (2) = - 16 + 4 + 8 \cdot 4 - 8$

Multiply $8$ by $4$ .

$f (2) = - 16 + 4 + 32 - 8$

Simplify by adding and subtracting.

Add $- 16$ and $4$ .

$f (2) = - 12 + 32 - 8$

Add $- 12$ and $32$ .

$f (2) = 20 - 8$

Subtract $8$ from $20$ .

$f (2) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

Step 4

Find the point at $x = 3$ .

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

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

Simplify the result.

Simplify each term.

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

$f (3) = - 2 \cdot 27 + 2 (3) + 8 {(3)}^{2} - 8$

Multiply $- 2$ by $27$ .

$f (3) = - 54 + 2 (3) + 8 {(3)}^{2} - 8$

Multiply $2$ by $3$ .

$f (3) = - 54 + 6 + 8 {(3)}^{2} - 8$

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

$f (3) = - 54 + 6 + 8 \cdot 9 - 8$

Multiply $8$ by $9$ .

$f (3) = - 54 + 6 + 72 - 8$

Simplify by adding and subtracting.

Add $- 54$ and $6$ .

$f (3) = - 48 + 72 - 8$

Add $- 48$ and $72$ .

$f (3) = 24 - 8$

Subtract $8$ from $24$ .

$f (3) = 16$

The final answer is $16$ .

$16$

Convert $16$ to decimal.

$y = 16$

Step 5

Find the point at $x = 4$ .

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

$f (4) = - 2 {(4)}^{3} + 2 (4) + 8 {(4)}^{2} - 8$

Simplify the result.

Simplify each term.

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

$f (4) = - 2 \cdot 64 + 2 (4) + 8 {(4)}^{2} - 8$

Multiply $- 2$ by $64$ .

$f (4) = - 128 + 2 (4) + 8 {(4)}^{2} - 8$

Multiply $2$ by $4$ .

$f (4) = - 128 + 8 + 8 {(4)}^{2} - 8$

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

$f (4) = - 128 + 8 + 8 \cdot 16 - 8$

Multiply $8$ by $16$ .

$f (4) = - 128 + 8 + 128 - 8$

Simplify by adding and subtracting.

Add $- 128$ and $8$ .

$f (4) = - 120 + 128 - 8$

Add $- 120$ and $128$ .

$f (4) = 8 - 8$

Subtract $8$ from $8$ .

$f (4) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 6

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

$\begin{array}{c} x & y \\ 0 & - 8 \\ 1 & 0 \\ 2 & 12 \\ 3 & 16 \\ 4 & 0 \end{array}$

Step 7

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ 0 & - 8 \\ 1 & 0 \\ 2 & 12 \\ 3 & 16 \\ 4 & 0 \end{array}$

Step 8

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

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