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

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

Step 1

Find the point at $x = 0$ .

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

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

Simplify the result.

Simplify each term.

Subtract $3$ from $0$ .

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

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

$f (0) = 0 \cdot 9 + 2 {((0) - 3)}^{2}$

Multiply $0$ by $9$ .

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

Subtract $3$ from $0$ .

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

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

$f (0) = 0 + 2 \cdot 9$

Multiply $2$ by $9$ .

$f (0) = 0 + 18$

Add $0$ and $18$ .

$f (0) = 18$

The final answer is $18$ .

$18$

Convert $18$ to decimal.

$y = 18$

Step 2

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify each term.

Multiply ${((1) - 3)}^{2}$ by $1$ .

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

Subtract $3$ from $1$ .

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

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

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

Subtract $3$ from $1$ .

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

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

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

Multiply $2$ by $4$ .

$f (1) = 4 + 8$

Add $4$ and $8$ .

$f (1) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

Step 3

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

Subtract $3$ from $2$ .

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

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

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

Multiply $2$ by $1$ .

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

Subtract $3$ from $2$ .

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

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

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

Multiply $2$ by $1$ .

$f (2) = 2 + 2$

Add $2$ and $2$ .

$f (2) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Step 4

Find the point at $x = 3$ .

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

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

Simplify the result.

Simplify each term.

Subtract $3$ from $3$ .

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

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

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

Multiply $3$ by $0$ .

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

Subtract $3$ from $3$ .

$f (3) = 0 + 2 \cdot 0^{2}$

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

$f (3) = 0 + 2 \cdot 0$

Multiply $2$ by $0$ .

$f (3) = 0 + 0$

Add $0$ and $0$ .

$f (3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 5

Find the point at $x = 4$ .

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

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

Simplify the result.

Simplify each term.

Subtract $3$ from $4$ .

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

One to any power is one.

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

Multiply $4$ by $1$ .

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

Subtract $3$ from $4$ .

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

One to any power is one.

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

Multiply $2$ by $1$ .

$f (4) = 4 + 2$

Add $4$ and $2$ .

$f (4) = 6$

The final answer is $6$ .

$6$

Convert $6$ to decimal.

$y = 6$

Step 6

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

$\begin{array}{c} x & y \\ 0 & 18 \\ 1 & 12 \\ 2 & 4 \\ 3 & 0 \\ 4 & 6 \end{array}$

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

$\begin{array}{c} x & y \\ 0 & 18 \\ 1 & 12 \\ 2 & 4 \\ 3 & 0 \\ 4 & 6 \end{array}$

Step 8

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

Related Questions

Support LCMGCF.com by disabling your adblocker.