Graph f(x)=-x(x-3)(5x+2)

$f (x) = - x (x - 3) (5 x + 2)$

Find the point at $x = - 1$ .

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

$f (- 1) = - 5 {(- 1)}^{3} + 13 {(- 1)}^{2} + 6 (- 1)$

Simplify the result.

Simplify each term.

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

$f (- 1) = - 5 \cdot - 1 + 13 {(- 1)}^{2} + 6 (- 1)$

Multiply $- 5$ by $- 1$ .

$f (- 1) = 5 + 13 {(- 1)}^{2} + 6 (- 1)$

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

$f (- 1) = 5 + 13 \cdot 1 + 6 (- 1)$

Multiply $13$ by $1$ .

$f (- 1) = 5 + 13 + 6 (- 1)$

Multiply $6$ by $- 1$ .

$f (- 1) = 5 + 13 - 6$

Simplify by adding and subtracting.

Add $5$ and $13$ .

$f (- 1) = 18 - 6$

Subtract $6$ from $18$ .

$f (- 1) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

Find the point at $x = 0$ .

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

$f (0) = - 5 {(0)}^{3} + 13 {(0)}^{2} + 6 (0)$

Simplify the result.

Simplify each term.

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

$f (0) = - 5 \cdot 0 + 13 {(0)}^{2} + 6 (0)$

Multiply $- 5$ by $0$ .

$f (0) = 0 + 13 {(0)}^{2} + 6 (0)$

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

$f (0) = 0 + 13 \cdot 0 + 6 (0)$

Multiply $13$ by $0$ .

$f (0) = 0 + 0 + 6 (0)$

Multiply $6$ 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.

$y = 0$

Find the point at $x = 1$ .

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

$f (1) = - 5 {(1)}^{3} + 13 {(1)}^{2} + 6 (1)$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = - 5 \cdot 1 + 13 {(1)}^{2} + 6 (1)$

Multiply $- 5$ by $1$ .

$f (1) = - 5 + 13 {(1)}^{2} + 6 (1)$

One to any power is one.

$f (1) = - 5 + 13 \cdot 1 + 6 (1)$

Multiply $13$ by $1$ .

$f (1) = - 5 + 13 + 6 (1)$

Multiply $6$ by $1$ .

$f (1) = - 5 + 13 + 6$

Simplify by adding numbers.

Add $- 5$ and $13$ .

$f (1) = 8 + 6$

Add $8$ and $6$ .

$f (1) = 14$

The final answer is $14$ .

$14$

Convert $14$ to decimal.

$y = 14$

Find the point at $x = 2$ .

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

$f (2) = - 5 {(2)}^{3} + 13 {(2)}^{2} + 6 (2)$

Simplify the result.

Simplify each term.

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

$f (2) = - 5 \cdot 8 + 13 {(2)}^{2} + 6 (2)$

Multiply $- 5$ by $8$ .

$f (2) = - 40 + 13 {(2)}^{2} + 6 (2)$

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

$f (2) = - 40 + 13 \cdot 4 + 6 (2)$

Multiply $13$ by $4$ .

$f (2) = - 40 + 52 + 6 (2)$

Multiply $6$ by $2$ .

$f (2) = - 40 + 52 + 12$

Simplify by adding numbers.

Add $- 40$ and $52$ .

$f (2) = 12 + 12$

Add $12$ and $12$ .

$f (2) = 24$

The final answer is $24$ .

$24$

Convert $24$ to decimal.

$y = 24$

Find the point at $x = 3$ .

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

$f (3) = - 5 {(3)}^{3} + 13 {(3)}^{2} + 6 (3)$

Simplify the result.

Simplify each term.

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

$f (3) = - 5 \cdot 27 + 13 {(3)}^{2} + 6 (3)$

Multiply $- 5$ by $27$ .

$f (3) = - 135 + 13 {(3)}^{2} + 6 (3)$

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

$f (3) = - 135 + 13 \cdot 9 + 6 (3)$

Multiply $13$ by $9$ .

$f (3) = - 135 + 117 + 6 (3)$

Multiply $6$ by $3$ .

$f (3) = - 135 + 117 + 18$

Simplify by adding numbers.

Add $- 135$ and $117$ .

$f (3) = - 18 + 18$

Add $- 18$ and $18$ .

$f (3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

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

$\begin{array}{c} x & y \\ - 1 & 12 \\ 0 & 0 \\ 1 & 14 \\ 2 & 24 \\ 3 & 0 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 1 & 12 \\ 0 & 0 \\ 1 & 14 \\ 2 & 24 \\ 3 & 0 \end{array}$

Graph f(x)=-x(x-3)(5x+2)

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