Graph f(x)=x^3-10x^2+9x

$f (x) = x^{3} - 10 x^{2} + 9 x$

Step 1

Find the point at $x = 2$ .

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

$f (2) = {(2)}^{3} - 10 {(2)}^{2} + 9 (2)$

Simplify the result.

Simplify each term.

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

$f (2) = 8 - 10 {(2)}^{2} + 9 (2)$

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

$f (2) = 8 - 10 \cdot 4 + 9 (2)$

Multiply $- 10$ by $4$ .

$f (2) = 8 - 40 + 9 (2)$

Multiply $9$ by $2$ .

$f (2) = 8 - 40 + 18$

Simplify by adding and subtracting.

Subtract $40$ from $8$ .

$f (2) = - 32 + 18$

Add $- 32$ and $18$ .

$f (2) = - 14$

The final answer is $- 14$ .

$- 14$

Convert $- 14$ to decimal.

$y = - 14$

Step 2

Find the point at $x = 3$ .

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

$f (3) = {(3)}^{3} - 10 {(3)}^{2} + 9 (3)$

Simplify the result.

Simplify each term.

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

$f (3) = 27 - 10 {(3)}^{2} + 9 (3)$

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

$f (3) = 27 - 10 \cdot 9 + 9 (3)$

Multiply $- 10$ by $9$ .

$f (3) = 27 - 90 + 9 (3)$

Multiply $9$ by $3$ .

$f (3) = 27 - 90 + 27$

Simplify by adding and subtracting.

Subtract $90$ from $27$ .

$f (3) = - 63 + 27$

Add $- 63$ and $27$ .

$f (3) = - 36$

The final answer is $- 36$ .

$- 36$

Convert $- 36$ to decimal.

$y = - 36$

Step 3

Find the point at $x = 4$ .

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

$f (4) = {(4)}^{3} - 10 {(4)}^{2} + 9 (4)$

Simplify the result.

Simplify each term.

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

$f (4) = 64 - 10 {(4)}^{2} + 9 (4)$

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

$f (4) = 64 - 10 \cdot 16 + 9 (4)$

Multiply $- 10$ by $16$ .

$f (4) = 64 - 160 + 9 (4)$

Multiply $9$ by $4$ .

$f (4) = 64 - 160 + 36$

Simplify by adding and subtracting.

Subtract $160$ from $64$ .

$f (4) = - 96 + 36$

Add $- 96$ and $36$ .

$f (4) = - 60$

The final answer is $- 60$ .

$- 60$

Convert $- 60$ to decimal.

$y = - 60$

Step 4

Find the point at $x = 5$ .

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

$f (5) = {(5)}^{3} - 10 {(5)}^{2} + 9 (5)$

Simplify the result.

Simplify each term.

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

$f (5) = 125 - 10 {(5)}^{2} + 9 (5)$

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

$f (5) = 125 - 10 \cdot 25 + 9 (5)$

Multiply $- 10$ by $25$ .

$f (5) = 125 - 250 + 9 (5)$

Multiply $9$ by $5$ .

$f (5) = 125 - 250 + 45$

Simplify by adding and subtracting.

Subtract $250$ from $125$ .

$f (5) = - 125 + 45$

Add $- 125$ and $45$ .

$f (5) = - 80$

The final answer is $- 80$ .

$- 80$

Convert $- 80$ to decimal.

$y = - 80$

Step 5

Find the point at $x = 6$ .

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

$f (6) = {(6)}^{3} - 10 {(6)}^{2} + 9 (6)$

Simplify the result.

Simplify each term.

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

$f (6) = 216 - 10 {(6)}^{2} + 9 (6)$

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

$f (6) = 216 - 10 \cdot 36 + 9 (6)$

Multiply $- 10$ by $36$ .

$f (6) = 216 - 360 + 9 (6)$

Multiply $9$ by $6$ .

$f (6) = 216 - 360 + 54$

Simplify by adding and subtracting.

Subtract $360$ from $216$ .

$f (6) = - 144 + 54$

Add $- 144$ and $54$ .

$f (6) = - 90$

The final answer is $- 90$ .

$- 90$

Convert $- 90$ to decimal.

$y = - 90$

Step 6

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

$\begin{array}{c} x & y \\ 2 & - 14 \\ 3 & - 36 \\ 4 & - 60 \\ 5 & - 80 \\ 6 & - 90 \end{array}$

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

$\begin{array}{c} x & y \\ 2 & - 14 \\ 3 & - 36 \\ 4 & - 60 \\ 5 & - 80 \\ 6 & - 90 \end{array}$

Step 8

Graph f(x)=x^3-10x^2+9x

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