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

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

Find the point at $x = - 1$ .

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

$f (- 1) = 2 {(- 1)}^{3} - 2 {(- 1)}^{2} - 4 \cdot - 1$

Simplify the result.

Simplify each term.

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

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

Multiply $2$ by $- 1$ .

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

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

$f (- 1) = - 2 - 2 \cdot 1 - 4 \cdot - 1$

Multiply $- 2$ by $1$ .

$f (- 1) = - 2 - 2 - 4 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$f (- 1) = - 2 - 2 + 4$

Simplify by adding and subtracting.

Subtract $2$ from $- 2$ .

$f (- 1) = - 4 + 4$

Add $- 4$ and $4$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 1$ .

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

$f (1) = 2 {(1)}^{3} - 2 {(1)}^{2} - 4 \cdot 1$

Simplify the result.

Simplify each term.

One to any power is one.

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

Multiply $2$ by $1$ .

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

One to any power is one.

$f (1) = 2 - 2 \cdot 1 - 4 \cdot 1$

Multiply $- 2$ by $1$ .

$f (1) = 2 - 2 - 4 \cdot 1$

Multiply $- 4$ by $1$ .

$f (1) = 2 - 2 - 4$

Simplify by subtracting numbers.

Subtract $2$ from $2$ .

$f (1) = 0 - 4$

Subtract $4$ from $0$ .

$f (1) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Find the point at $x = 2$ .

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

$f (2) = 2 {(2)}^{3} - 2 {(2)}^{2} - 4 \cdot 2$

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 $1$ .

$f (2) = 2 {(2)}^{3} - 2 {(2)}^{2} - 4 \cdot 2$

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

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

Add $1$ and $3$ .

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

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

$f (2) = 16 - 2 {(2)}^{2} - 4 \cdot 2$

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

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

Multiply $- 2$ by $4$ .

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

Multiply $- 4$ by $2$ .

$f (2) = 16 - 8 - 8$

Simplify by subtracting numbers.

Subtract $8$ from $16$ .

$f (2) = 8 - 8$

Subtract $8$ from $8$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 3$ .

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

$f (3) = 2 {(3)}^{3} - 2 {(3)}^{2} - 4 \cdot 3$

Simplify the result.

Simplify each term.

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

$f (3) = 2 \cdot 27 - 2 {(3)}^{2} - 4 \cdot 3$

Multiply $2$ by $27$ .

$f (3) = 54 - 2 {(3)}^{2} - 4 \cdot 3$

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

$f (3) = 54 - 2 \cdot 9 - 4 \cdot 3$

Multiply $- 2$ by $9$ .

$f (3) = 54 - 18 - 4 \cdot 3$

Multiply $- 4$ by $3$ .

$f (3) = 54 - 18 - 12$

Simplify by subtracting numbers.

Subtract $18$ from $54$ .

$f (3) = 36 - 12$

Subtract $12$ from $36$ .

$f (3) = 24$

The final answer is $24$ .

$24$

Convert $24$ to decimal.

$y = 24$

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

$\begin{array}{c} x & y \\ - 1 & 0 \\ 0 & 0 \\ 1 & - 4 \\ 2 & 0 \\ 3 & 24 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 1 & 0 \\ 0 & 0 \\ 1 & - 4 \\ 2 & 0 \\ 3 & 24 \end{array}$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.