Graph f(x)=-0.08x(x^2-11x+18)

$f (x) = - 0.08 x (x^{2} - 11 x + 18)$

Step 1

Find the point at $x = 2$ .

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

$f (2) = - 0.08 {(2)}^{3} + 0.88 {(2)}^{2} - 1.44 \cdot 2$

Simplify the result.

Simplify each term.

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

$f (2) = - 0.08 \cdot 8 + 0.88 {(2)}^{2} - 1.44 \cdot 2$

Multiply $- 0.08$ by $8$ .

$f (2) = - 0.64 + 0.88 {(2)}^{2} - 1.44 \cdot 2$

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

$f (2) = - 0.64 + 0.88 \cdot 4 - 1.44 \cdot 2$

Multiply $0.88$ by $4$ .

$f (2) = - 0.64 + 3.52 - 1.44 \cdot 2$

Multiply $- 1.44$ by $2$ .

$f (2) = - 0.64 + 3.52 - 2.88$

Simplify by adding and subtracting.

Add $- 0.64$ and $3.52$ .

$f (2) = 2.88 - 2.88$

Subtract $2.88$ from $2.88$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Step 2

Find the point at $x = 3$ .

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

$f (3) = - 0.08 {(3)}^{3} + 0.88 {(3)}^{2} - 1.44 \cdot 3$

Simplify the result.

Simplify each term.

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

$f (3) = - 0.08 \cdot 27 + 0.88 {(3)}^{2} - 1.44 \cdot 3$

Multiply $- 0.08$ by $27$ .

$f (3) = - 2.16 + 0.88 {(3)}^{2} - 1.44 \cdot 3$

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

$f (3) = - 2.16 + 0.88 \cdot 9 - 1.44 \cdot 3$

Multiply $0.88$ by $9$ .

$f (3) = - 2.16 + 7.92 - 1.44 \cdot 3$

Multiply $- 1.44$ by $3$ .

$f (3) = - 2.16 + 7.92 - 4.32$

Simplify by adding and subtracting.

Add $- 2.16$ and $7.92$ .

$f (3) = 5.76 - 4.32$

Subtract $4.32$ from $5.76$ .

$f (3) = 1.44$

The final answer is $1.44$ .

$1.44$

Step 3

Find the point at $x = 4$ .

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

$f (4) = - 0.08 {(4)}^{3} + 0.88 {(4)}^{2} - 1.44 \cdot 4$

Simplify the result.

Simplify each term.

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

$f (4) = - 0.08 \cdot 64 + 0.88 {(4)}^{2} - 1.44 \cdot 4$

Multiply $- 0.08$ by $64$ .

$f (4) = - 5.12 + 0.88 {(4)}^{2} - 1.44 \cdot 4$

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

$f (4) = - 5.12 + 0.88 \cdot 16 - 1.44 \cdot 4$

Multiply $0.88$ by $16$ .

$f (4) = - 5.12 + 14.08 - 1.44 \cdot 4$

Multiply $- 1.44$ by $4$ .

$f (4) = - 5.12 + 14.08 - 5.76$

Simplify by adding and subtracting.

Add $- 5.12$ and $14.08$ .

$f (4) = 8.96 - 5.76$

Subtract $5.76$ from $8.96$ .

$f (4) = 3.2$

The final answer is $3.2$ .

$3.2$

Step 4

Find the point at $x = 5$ .

Replace the variable $x$ with $5$ in the expression.

$f (5) = - 0.08 {(5)}^{3} + 0.88 {(5)}^{2} - 1.44 \cdot 5$

Simplify the result.

Simplify each term.

Raise $5$ to the power of $3$ .

$f (5) = - 0.08 \cdot 125 + 0.88 {(5)}^{2} - 1.44 \cdot 5$

Multiply $- 0.08$ by $125$ .

$f (5) = - 10 + 0.88 {(5)}^{2} - 1.44 \cdot 5$

Raise $5$ to the power of $2$ .

$f (5) = - 10 + 0.88 \cdot 25 - 1.44 \cdot 5$

Multiply $0.88$ by $25$ .

$f (5) = - 10 + 22 - 1.44 \cdot 5$

Multiply $- 1.44$ by $5$ .

$f (5) = - 10 + 22 - 7.2$

Simplify by adding and subtracting.

Add $- 10$ and $22$ .

$f (5) = 12 - 7.2$

Subtract $7.2$ from $12$ .

$f (5) = 4.8$

The final answer is $4.8$ .

$4.8$

Step 5

Find the point at $x = 6$ .

Replace the variable $x$ with $6$ in the expression.

$f (6) = - 0.08 {(6)}^{3} + 0.88 {(6)}^{2} - 1.44 \cdot 6$

Simplify the result.

Simplify each term.

Raise $6$ to the power of $3$ .

$f (6) = - 0.08 \cdot 216 + 0.88 {(6)}^{2} - 1.44 \cdot 6$

Multiply $- 0.08$ by $216$ .

$f (6) = - 17.28 + 0.88 {(6)}^{2} - 1.44 \cdot 6$

Raise $6$ to the power of $2$ .

$f (6) = - 17.28 + 0.88 \cdot 36 - 1.44 \cdot 6$

Multiply $0.88$ by $36$ .

$f (6) = - 17.28 + 31.68 - 1.44 \cdot 6$

Multiply $- 1.44$ by $6$ .

$f (6) = - 17.28 + 31.68 - 8.64$

Simplify by adding and subtracting.

Add $- 17.28$ and $31.68$ .

$f (6) = 14.4 - 8.64$

Subtract $8.64$ from $14.4$ .

$f (6) = 5.76$

The final answer is $5.76$ .

$5.76$

Step 6

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

$\begin{array}{c} x & y \\ 2 & 0 \\ 3 & 1.44 \\ 4 & 3.2 \\ 5 & 4.8 \\ 6 & 5.76 \end{array}$

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

$\begin{array}{c} x & y \\ 2 & 0 \\ 3 & 1.44 \\ 4 & 3.2 \\ 5 & 4.8 \\ 6 & 5.76 \end{array}$

Step 8

Graph f(x)=-0.08x(x^2-11x+18)

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