Graph y=(x+3)(x-3)(x-4)

$y = (x + 3) (x - 3) (x - 4)$

Step 1

Find the point at $x = 0$ .

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

$f (0) = {(0)}^{3} - 4 {(0)}^{2} - 9 \cdot 0 + 36$

Simplify the result.

Simplify each term.

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

$f (0) = 0 - 4 {(0)}^{2} - 9 \cdot 0 + 36$

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

$f (0) = 0 - 4 \cdot 0 - 9 \cdot 0 + 36$

Multiply $- 4$ by $0$ .

$f (0) = 0 + 0 - 9 \cdot 0 + 36$

Multiply $- 9$ by $0$ .

$f (0) = 0 + 0 + 0 + 36$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0 + 36$

Add $0$ and $0$ .

$f (0) = 0 + 36$

Add $0$ and $36$ .

$f (0) = 36$

The final answer is $36$ .

$36$

Convert $36$ to decimal.

$y = 36$

Step 2

Find the point at $x = 1$ .

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

$f (1) = {(1)}^{3} - 4 {(1)}^{2} - 9 \cdot 1 + 36$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 1 - 4 {(1)}^{2} - 9 \cdot 1 + 36$

One to any power is one.

$f (1) = 1 - 4 \cdot 1 - 9 \cdot 1 + 36$

Multiply $- 4$ by $1$ .

$f (1) = 1 - 4 - 9 \cdot 1 + 36$

Multiply $- 9$ by $1$ .

$f (1) = 1 - 4 - 9 + 36$

Simplify by adding and subtracting.

Subtract $4$ from $1$ .

$f (1) = - 3 - 9 + 36$

Subtract $9$ from $- 3$ .

$f (1) = - 12 + 36$

Add $- 12$ and $36$ .

$f (1) = 24$

The final answer is $24$ .

$24$

Convert $24$ to decimal.

$y = 24$

Step 3

Find the point at $x = 2$ .

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

$f (2) = {(2)}^{3} - 4 {(2)}^{2} - 9 \cdot 2 + 36$

Simplify the result.

Simplify each term.

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

$f (2) = 8 - 4 {(2)}^{2} - 9 \cdot 2 + 36$

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

$f (2) = 8 - 4 \cdot 4 - 9 \cdot 2 + 36$

Multiply $- 4$ by $4$ .

$f (2) = 8 - 16 - 9 \cdot 2 + 36$

Multiply $- 9$ by $2$ .

$f (2) = 8 - 16 - 18 + 36$

Simplify by adding and subtracting.

Subtract $16$ from $8$ .

$f (2) = - 8 - 18 + 36$

Subtract $18$ from $- 8$ .

$f (2) = - 26 + 36$

Add $- 26$ and $36$ .

$f (2) = 10$

The final answer is $10$ .

$10$

Convert $10$ to decimal.

$y = 10$

Step 4

Find the point at $x = 3$ .

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

$f (3) = {(3)}^{3} - 4 {(3)}^{2} - 9 \cdot 3 + 36$

Simplify the result.

Simplify each term.

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

$f (3) = 27 - 4 {(3)}^{2} - 9 \cdot 3 + 36$

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

$f (3) = 27 - 4 \cdot 9 - 9 \cdot 3 + 36$

Multiply $- 4$ by $9$ .

$f (3) = 27 - 36 - 9 \cdot 3 + 36$

Multiply $- 9$ by $3$ .

$f (3) = 27 - 36 - 27 + 36$

Simplify by adding and subtracting.

Subtract $36$ from $27$ .

$f (3) = - 9 - 27 + 36$

Subtract $27$ from $- 9$ .

$f (3) = - 36 + 36$

Add $- 36$ and $36$ .

$f (3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 5

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

$\begin{array}{c} x & y \\ 0 & 36 \\ 1 & 24 \\ 2 & 10 \\ 3 & 0 \\ 4 & 0 \end{array}$

Step 6

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ 0 & 36 \\ 1 & 24 \\ 2 & 10 \\ 3 & 0 \\ 4 & 0 \end{array}$

Step 7

Graph y=(x+3)(x-3)(x-4)

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