Graph y=x(x-2)(x+5)

$y = x (x - 2) (x + 5)$

Step 1

Find the point at $x = - 3$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

Multiply $3$ by $9$ .

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

Multiply $- 10$ by $- 3$ .

$f (- 3) = - 27 + 27 + 30$

Simplify by adding numbers.

Add $- 27$ and $27$ .

$f (- 3) = 0 + 30$

Add $0$ and $30$ .

$f (- 3) = 30$

The final answer is $30$ .

$30$

Convert $30$ to decimal.

$y = 30$

Step 2

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

$f (- 2) = - 8 + 3 {(- 2)}^{2} - 10 \cdot - 2$

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

$f (- 2) = - 8 + 3 \cdot 4 - 10 \cdot - 2$

Multiply $3$ by $4$ .

$f (- 2) = - 8 + 12 - 10 \cdot - 2$

Multiply $- 10$ by $- 2$ .

$f (- 2) = - 8 + 12 + 20$

Simplify by adding numbers.

Add $- 8$ and $12$ .

$f (- 2) = 4 + 20$

Add $4$ and $20$ .

$f (- 2) = 24$

The final answer is $24$ .

$24$

Convert $24$ to decimal.

$y = 24$

Step 3

Find the point at $x = - 1$ .

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

$f (- 1) = {(- 1)}^{3} + 3 {(- 1)}^{2} - 10 \cdot - 1$

Simplify the result.

Simplify each term.

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

$f (- 1) = - 1 + 3 {(- 1)}^{2} - 10 \cdot - 1$

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

$f (- 1) = - 1 + 3 \cdot 1 - 10 \cdot - 1$

Multiply $3$ by $1$ .

$f (- 1) = - 1 + 3 - 10 \cdot - 1$

Multiply $- 10$ by $- 1$ .

$f (- 1) = - 1 + 3 + 10$

Simplify by adding numbers.

Add $- 1$ and $3$ .

$f (- 1) = 2 + 10$

Add $2$ and $10$ .

$f (- 1) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

Step 4

Find the point at $x = 0$ .

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

$f (0) = {(0)}^{3} + 3 {(0)}^{2} - 10 \cdot 0$

Simplify the result.

Simplify each term.

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

$f (0) = 0 + 3 {(0)}^{2} - 10 \cdot 0$

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

$f (0) = 0 + 3 \cdot 0 - 10 \cdot 0$

Multiply $3$ by $0$ .

$f (0) = 0 + 0 - 10 \cdot 0$

Multiply $- 10$ 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 5

Find the point at $x = 1$ .

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

$f (1) = {(1)}^{3} + 3 {(1)}^{2} - 10 \cdot 1$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 1 + 3 {(1)}^{2} - 10 \cdot 1$

One to any power is one.

$f (1) = 1 + 3 \cdot 1 - 10 \cdot 1$

Multiply $3$ by $1$ .

$f (1) = 1 + 3 - 10 \cdot 1$

Multiply $- 10$ by $1$ .

$f (1) = 1 + 3 - 10$

Simplify by adding and subtracting.

Add $1$ and $3$ .

$f (1) = 4 - 10$

Subtract $10$ from $4$ .

$f (1) = - 6$

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.

$\begin{array}{c} x & y \\ - 3 & 30 \\ - 2 & 24 \\ - 1 & 12 \\ 0 & 0 \\ 1 & - 6 \end{array}$

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

$\begin{array}{c} x & y \\ - 3 & 30 \\ - 2 & 24 \\ - 1 & 12 \\ 0 & 0 \\ 1 & - 6 \end{array}$

Step 8

Graph y=x(x-2)(x+5)

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