Graph y=x(x+5)(x-8)

$y = x (x + 5) (x - 8)$

Step 1

Find the point at $x = - 1$ .

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

$f (- 1) = {(- 1)}^{3} - 3 {(- 1)}^{2} - 40 \cdot - 1$

Simplify the result.

Simplify each term.

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

$f (- 1) = - 1 - 3 {(- 1)}^{2} - 40 \cdot - 1$

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

$f (- 1) = - 1 - 3 \cdot 1 - 40 \cdot - 1$

Multiply $- 3$ by $1$ .

$f (- 1) = - 1 - 3 - 40 \cdot - 1$

Multiply $- 40$ by $- 1$ .

$f (- 1) = - 1 - 3 + 40$

Simplify by adding and subtracting.

Subtract $3$ from $- 1$ .

$f (- 1) = - 4 + 40$

Add $- 4$ and $40$ .

$f (- 1) = 36$

The final answer is $36$ .

$36$

Convert $36$ to decimal.

$y = 36$

Step 2

Find the point at $x = 0$ .

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

$f (0) = {(0)}^{3} - 3 {(0)}^{2} - 40 \cdot 0$

Simplify the result.

Simplify each term.

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

$f (0) = 0 - 3 {(0)}^{2} - 40 \cdot 0$

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

$f (0) = 0 - 3 \cdot 0 - 40 \cdot 0$

Multiply $- 3$ by $0$ .

$f (0) = 0 + 0 - 40 \cdot 0$

Multiply $- 40$ by $0$ .

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

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0$

Add $0$ and $0$ .

$f (0) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 1$ .

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

$f (1) = {(1)}^{3} - 3 {(1)}^{2} - 40 \cdot 1$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 1 - 3 {(1)}^{2} - 40 \cdot 1$

One to any power is one.

$f (1) = 1 - 3 \cdot 1 - 40 \cdot 1$

Multiply $- 3$ by $1$ .

$f (1) = 1 - 3 - 40 \cdot 1$

Multiply $- 40$ by $1$ .

$f (1) = 1 - 3 - 40$

Simplify by subtracting numbers.

Subtract $3$ from $1$ .

$f (1) = - 2 - 40$

Subtract $40$ from $- 2$ .

$f (1) = - 42$

The final answer is $- 42$ .

$- 42$

Convert $- 42$ to decimal.

$y = - 42$

Step 4

Find the point at $x = 2$ .

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

$f (2) = {(2)}^{3} - 3 {(2)}^{2} - 40 \cdot 2$

Simplify the result.

Simplify each term.

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

$f (2) = 8 - 3 {(2)}^{2} - 40 \cdot 2$

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

$f (2) = 8 - 3 \cdot 4 - 40 \cdot 2$

Multiply $- 3$ by $4$ .

$f (2) = 8 - 12 - 40 \cdot 2$

Multiply $- 40$ by $2$ .

$f (2) = 8 - 12 - 80$

Simplify by subtracting numbers.

Subtract $12$ from $8$ .

$f (2) = - 4 - 80$

Subtract $80$ from $- 4$ .

$f (2) = - 84$

The final answer is $- 84$ .

$- 84$

Convert $- 84$ to decimal.

$y = - 84$

Step 5

Find the point at $x = 3$ .

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

$f (3) = {(3)}^{3} - 3 {(3)}^{2} - 40 \cdot 3$

Simplify the result.

Simplify each term.

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

$f (3) = 27 - 3 {(3)}^{2} - 40 \cdot 3$

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

$f (3) = 27 - 3 \cdot 9 - 40 \cdot 3$

Multiply $- 3$ by $9$ .

$f (3) = 27 - 27 - 40 \cdot 3$

Multiply $- 40$ by $3$ .

$f (3) = 27 - 27 - 120$

Simplify by subtracting numbers.

Subtract $27$ from $27$ .

$f (3) = 0 - 120$

Subtract $120$ from $0$ .

$f (3) = - 120$

The final answer is $- 120$ .

$- 120$

Convert $- 120$ to decimal.

$y = - 120$

Step 6

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

$\begin{array}{c} x & y \\ - 1 & 36 \\ 0 & 0 \\ 1 & - 42 \\ 2 & - 84 \\ 3 & - 120 \end{array}$

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

$\begin{array}{c} x & y \\ - 1 & 36 \\ 0 & 0 \\ 1 & - 42 \\ 2 & - 84 \\ 3 & - 120 \end{array}$

Step 8

Graph y=x(x+5)(x-8)

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