Graph y=-x(1-x)(x-2)

$y = - x (1 - x) (x - 2)$

Step 1

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 3$ by $1$ .

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

Multiply $2$ by $- 1$ .

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

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

$f (- 1) = - 3 - 2 - 1$

Simplify by subtracting numbers.

Subtract $2$ from $- 3$ .

$f (- 1) = - 5 - 1$

Subtract $1$ from $- 5$ .

$f (- 1) = - 6$

The final answer is $- 6$ .

$- 6$

Convert $- 6$ to decimal.

$y = - 6$

Step 2

Find the point at $x = 0$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 3$ by $0$ .

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

Multiply $2$ by $0$ .

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

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

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

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 $x = 3$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 3$ by $9$ .

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

Multiply $2$ by $3$ .

$f (3) = - 27 + 6 + {(3)}^{3}$

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

$f (3) = - 27 + 6 + 27$

Simplify by adding numbers.

Add $- 27$ and $6$ .

$f (3) = - 21 + 27$

Add $- 21$ and $27$ .

$f (3) = 6$

The final answer is $6$ .

$6$

Convert $6$ to decimal.

$y = 6$

Step 4

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

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

Step 5

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

Falls to the left and rises to the right

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

Step 6

Graph y=-x(1-x)(x-2)

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