Graph p(x)=(x+2)(2x-3)(x-3)

$p (x) = (x + 2) (2 x - 3) (x - 3)$

Step 1

Find the point at $x = - 1$ .

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

$f (- 1) = 2 {(- 1)}^{3} - 5 {(- 1)}^{2} - 9 \cdot - 1 + 18$

Simplify the result.

Simplify each term.

Raise $- 1$ to the power of $3$ .

$f (- 1) = 2 \cdot - 1 - 5 {(- 1)}^{2} - 9 \cdot - 1 + 18$

Multiply $2$ by $- 1$ .

$f (- 1) = - 2 - 5 {(- 1)}^{2} - 9 \cdot - 1 + 18$

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

$f (- 1) = - 2 - 5 \cdot 1 - 9 \cdot - 1 + 18$

Multiply $- 5$ by $1$ .

$f (- 1) = - 2 - 5 - 9 \cdot - 1 + 18$

Multiply $- 9$ by $- 1$ .

$f (- 1) = - 2 - 5 + 9 + 18$

Simplify by adding and subtracting.

Subtract $5$ from $- 2$ .

$f (- 1) = - 7 + 9 + 18$

Add $- 7$ and $9$ .

$f (- 1) = 2 + 18$

Add $2$ and $18$ .

$f (- 1) = 20$

The final answer is $20$ .

$20$

Convert $20$ to decimal.

$y = 20$

Step 2

Find the point at $x = 0$ .

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

$f (0) = 2 {(0)}^{3} - 5 {(0)}^{2} - 9 \cdot 0 + 18$

Simplify the result.

Simplify each term.

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

$f (0) = 2 \cdot 0 - 5 {(0)}^{2} - 9 \cdot 0 + 18$

Multiply $2$ by $0$ .

$f (0) = 0 - 5 {(0)}^{2} - 9 \cdot 0 + 18$

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

$f (0) = 0 - 5 \cdot 0 - 9 \cdot 0 + 18$

Multiply $- 5$ by $0$ .

$f (0) = 0 + 0 - 9 \cdot 0 + 18$

Multiply $- 9$ by $0$ .

$f (0) = 0 + 0 + 0 + 18$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0 + 18$

Add $0$ and $0$ .

$f (0) = 0 + 18$

Add $0$ and $18$ .

$f (0) = 18$

The final answer is $18$ .

$18$

Convert $18$ to decimal.

$y = 18$

Step 3

Find the point at $x = 1$ .

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

$f (1) = 2 {(1)}^{3} - 5 {(1)}^{2} - 9 \cdot 1 + 18$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 2 \cdot 1 - 5 {(1)}^{2} - 9 \cdot 1 + 18$

Multiply $2$ by $1$ .

$f (1) = 2 - 5 {(1)}^{2} - 9 \cdot 1 + 18$

One to any power is one.

$f (1) = 2 - 5 \cdot 1 - 9 \cdot 1 + 18$

Multiply $- 5$ by $1$ .

$f (1) = 2 - 5 - 9 \cdot 1 + 18$

Multiply $- 9$ by $1$ .

$f (1) = 2 - 5 - 9 + 18$

Simplify by adding and subtracting.

Subtract $5$ from $2$ .

$f (1) = - 3 - 9 + 18$

Subtract $9$ from $- 3$ .

$f (1) = - 12 + 18$

Add $- 12$ and $18$ .

$f (1) = 6$

The final answer is $6$ .

$6$

Convert $6$ to decimal.

$y = 6$

Step 4

Find the point at $x = 2$ .

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

$f (2) = 2 {(2)}^{3} - 5 {(2)}^{2} - 9 \cdot 2 + 18$

Simplify the result.

Simplify each term.

Multiply $2$ by ${(2)}^{3}$ by adding the exponents.

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

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

$f (2) = 2 {(2)}^{3} - 5 {(2)}^{2} - 9 \cdot 2 + 18$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (2) = 2^{1 + 3} - 5 {(2)}^{2} - 9 \cdot 2 + 18$

Add $1$ and $3$ .

$f (2) = 2^{4} - 5 {(2)}^{2} - 9 \cdot 2 + 18$

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

$f (2) = 16 - 5 {(2)}^{2} - 9 \cdot 2 + 18$

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

$f (2) = 16 - 5 \cdot 4 - 9 \cdot 2 + 18$

Multiply $- 5$ by $4$ .

$f (2) = 16 - 20 - 9 \cdot 2 + 18$

Multiply $- 9$ by $2$ .

$f (2) = 16 - 20 - 18 + 18$

Simplify by adding and subtracting.

Subtract $20$ from $16$ .

$f (2) = - 4 - 18 + 18$

Subtract $18$ from $- 4$ .

$f (2) = - 22 + 18$

Add $- 22$ and $18$ .

$f (2) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Step 5

Find the point at $x = 3$ .

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

$f (3) = 2 {(3)}^{3} - 5 {(3)}^{2} - 9 \cdot 3 + 18$

Simplify the result.

Simplify each term.

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

$f (3) = 2 \cdot 27 - 5 {(3)}^{2} - 9 \cdot 3 + 18$

Multiply $2$ by $27$ .

$f (3) = 54 - 5 {(3)}^{2} - 9 \cdot 3 + 18$

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

$f (3) = 54 - 5 \cdot 9 - 9 \cdot 3 + 18$

Multiply $- 5$ by $9$ .

$f (3) = 54 - 45 - 9 \cdot 3 + 18$

Multiply $- 9$ by $3$ .

$f (3) = 54 - 45 - 27 + 18$

Simplify by adding and subtracting.

Subtract $45$ from $54$ .

$f (3) = 9 - 27 + 18$

Subtract $27$ from $9$ .

$f (3) = - 18 + 18$

Add $- 18$ and $18$ .

$f (3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 6

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

$\begin{array}{c} x & y \\ - 1 & 20 \\ 0 & 18 \\ 1 & 6 \\ 2 & - 4 \\ 3 & 0 \end{array}$

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

$\begin{array}{c} x & y \\ - 1 & 20 \\ 0 & 18 \\ 1 & 6 \\ 2 & - 4 \\ 3 & 0 \end{array}$

Step 8

Graph p(x)=(x+2)(2x-3)(x-3)

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