Graph f(x)=0.2(x-2)(x+1)(x-5)

$f (x) = 0.2 (x - 2) (x + 1) (x - 5)$

Step 1

Find the point at $x = 0$ .

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

$f (0) = 0.2 {(0)}^{3} - 1.2 {(0)}^{2} + 0.6 (0) + 2$

Simplify the result.

Simplify each term.

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

$f (0) = 0.2 \cdot 0 - 1.2 {(0)}^{2} + 0.6 (0) + 2$

Multiply $0.2$ by $0$ .

$f (0) = 0 - 1.2 {(0)}^{2} + 0.6 (0) + 2$

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

$f (0) = 0 - 1.2 \cdot 0 + 0.6 (0) + 2$

Multiply $- 1.2$ by $0$ .

$f (0) = 0 + 0 + 0.6 (0) + 2$

Multiply $0.6$ by $0$ .

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

Simplify by adding numbers.

Add $0$ and $0$ .

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

Add $0$ and $0$ .

$f (0) = 0 + 2$

Add $0$ and $2$ .

$f (0) = 2$

The final answer is $2$ .

$2$

Step 2

Find the point at $x = 1$ .

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

$f (1) = 0.2 {(1)}^{3} - 1.2 {(1)}^{2} + 0.6 (1) + 2$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 0.2 \cdot 1 - 1.2 {(1)}^{2} + 0.6 (1) + 2$

Multiply $0.2$ by $1$ .

$f (1) = 0.2 - 1.2 {(1)}^{2} + 0.6 (1) + 2$

One to any power is one.

$f (1) = 0.2 - 1.2 \cdot 1 + 0.6 (1) + 2$

Multiply $- 1.2$ by $1$ .

$f (1) = 0.2 - 1.2 + 0.6 (1) + 2$

Multiply $0.6$ by $1$ .

$f (1) = 0.2 - 1.2 + 0.6 + 2$

Simplify by adding and subtracting.

Subtract $1.2$ from $0.2$ .

$f (1) = - 1 + 0.6 + 2$

Add $- 1$ and $0.6$ .

$f (1) = - 0.4 + 2$

Add $- 0.4$ and $2$ .

$f (1) = 1.6$

The final answer is $1.6$ .

$1.6$

Step 3

Find the point at $x = 2$ .

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

$f (2) = 0.2 {(2)}^{3} - 1.2 {(2)}^{2} + 0.6 (2) + 2$

Simplify the result.

Simplify each term.

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

$f (2) = 0.2 \cdot 8 - 1.2 {(2)}^{2} + 0.6 (2) + 2$

Multiply $0.2$ by $8$ .

$f (2) = 1.6 - 1.2 {(2)}^{2} + 0.6 (2) + 2$

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

$f (2) = 1.6 - 1.2 \cdot 4 + 0.6 (2) + 2$

Multiply $- 1.2$ by $4$ .

$f (2) = 1.6 - 4.8 + 0.6 (2) + 2$

Multiply $0.6$ by $2$ .

$f (2) = 1.6 - 4.8 + 1.2 + 2$

Simplify by adding and subtracting.

Subtract $4.8$ from $1.6$ .

$f (2) = - 3.2 + 1.2 + 2$

Add $- 3.2$ and $1.2$ .

$f (2) = - 2 + 2$

Add $- 2$ and $2$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Step 4

Find the point at $x = 3$ .

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

$f (3) = 0.2 {(3)}^{3} - 1.2 {(3)}^{2} + 0.6 (3) + 2$

Simplify the result.

Simplify each term.

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

$f (3) = 0.2 \cdot 27 - 1.2 {(3)}^{2} + 0.6 (3) + 2$

Multiply $0.2$ by $27$ .

$f (3) = 5.4 - 1.2 {(3)}^{2} + 0.6 (3) + 2$

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

$f (3) = 5.4 - 1.2 \cdot 9 + 0.6 (3) + 2$

Multiply $- 1.2$ by $9$ .

$f (3) = 5.4 - 10.8 + 0.6 (3) + 2$

Multiply $0.6$ by $3$ .

$f (3) = 5.4 - 10.8 + 1.8 + 2$

Simplify by adding and subtracting.

Subtract $10.8$ from $5.4$ .

$f (3) = - 5.4 + 1.8 + 2$

Add $- 5.4$ and $1.8$ .

$f (3) = - 3.6 + 2$

Add $- 3.6$ and $2$ .

$f (3) = - 1.6$

The final answer is $- 1.6$ .

$- 1.6$

Step 5

Find the point at $x = 4$ .

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

$f (4) = 0.2 {(4)}^{3} - 1.2 {(4)}^{2} + 0.6 (4) + 2$

Simplify the result.

Simplify each term.

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

$f (4) = 0.2 \cdot 64 - 1.2 {(4)}^{2} + 0.6 (4) + 2$

Multiply $0.2$ by $64$ .

$f (4) = 12.8 - 1.2 {(4)}^{2} + 0.6 (4) + 2$

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

$f (4) = 12.8 - 1.2 \cdot 16 + 0.6 (4) + 2$

Multiply $- 1.2$ by $16$ .

$f (4) = 12.8 - 19.2 + 0.6 (4) + 2$

Multiply $0.6$ by $4$ .

$f (4) = 12.8 - 19.2 + 2.4 + 2$

Simplify by adding and subtracting.

Subtract $19.2$ from $12.8$ .

$f (4) = - 6.4 + 2.4 + 2$

Add $- 6.4$ and $2.4$ .

$f (4) = - 4 + 2$

Add $- 4$ and $2$ .

$f (4) = - 2$

The final answer is $- 2$ .

$- 2$

Step 6

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

$\begin{array}{c} x & y \\ 0 & 2 \\ 1 & 1.6 \\ 2 & 0 \\ 3 & - 1.6 \\ 4 & - 2 \end{array}$

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

$\begin{array}{c} x & y \\ 0 & 2 \\ 1 & 1.6 \\ 2 & 0 \\ 3 & - 1.6 \\ 4 & - 2 \end{array}$

Step 8

Graph f(x)=0.2(x-2)(x+1)(x-5)

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