Graph y=-4x(x-1)(x-2)

$y = - 4 x (x - 1) (x - 2)$

Step 1

Find the point at $x = - 1$ .

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

$f (- 1) = - 4 {(- 1)}^{3} + 12 {(- 1)}^{2} - 8 \cdot - 1$

Simplify the result.

Simplify each term.

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

$f (- 1) = - 4 \cdot - 1 + 12 {(- 1)}^{2} - 8 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$f (- 1) = 4 + 12 {(- 1)}^{2} - 8 \cdot - 1$

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

$f (- 1) = 4 + 12 \cdot 1 - 8 \cdot - 1$

Multiply $12$ by $1$ .

$f (- 1) = 4 + 12 - 8 \cdot - 1$

Multiply $- 8$ by $- 1$ .

$f (- 1) = 4 + 12 + 8$

Simplify by adding numbers.

Add $4$ and $12$ .

$f (- 1) = 16 + 8$

Add $16$ and $8$ .

$f (- 1) = 24$

The final answer is $24$ .

$24$

Convert $24$ to decimal.

$y = 24$

Step 2

Find the point at $x = 0$ .

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

$f (0) = - 4 {(0)}^{3} + 12 {(0)}^{2} - 8 \cdot 0$

Simplify the result.

Simplify each term.

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

$f (0) = - 4 \cdot 0 + 12 {(0)}^{2} - 8 \cdot 0$

Multiply $- 4$ by $0$ .

$f (0) = 0 + 12 {(0)}^{2} - 8 \cdot 0$

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

$f (0) = 0 + 12 \cdot 0 - 8 \cdot 0$

Multiply $12$ by $0$ .

$f (0) = 0 + 0 - 8 \cdot 0$

Multiply $- 8$ 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 $x = 3$ .

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

$f (3) = - 4 {(3)}^{3} + 12 {(3)}^{2} - 8 \cdot 3$

Simplify the result.

Simplify each term.

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

$f (3) = - 4 \cdot 27 + 12 {(3)}^{2} - 8 \cdot 3$

Multiply $- 4$ by $27$ .

$f (3) = - 108 + 12 {(3)}^{2} - 8 \cdot 3$

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

$f (3) = - 108 + 12 \cdot 9 - 8 \cdot 3$

Multiply $12$ by $9$ .

$f (3) = - 108 + 108 - 8 \cdot 3$

Multiply $- 8$ by $3$ .

$f (3) = - 108 + 108 - 24$

Simplify by adding and subtracting.

Add $- 108$ and $108$ .

$f (3) = 0 - 24$

Subtract $24$ from $0$ .

$f (3) = - 24$

The final answer is $- 24$ .

$- 24$

Convert $- 24$ to decimal.

$y = - 24$

Step 4

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

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

Step 5

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

Rises to the left and falls to the right

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

Step 6

Graph y=-4x(x-1)(x-2)

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