Graph c(x)=2+3x^2-x^3

$c (x) = 2 + 3 x^{2} - x^{3}$

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $3$ by $1$ .

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

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

Multiply $- 1$ by ${(- 1)}^{3}$ .

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

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $3$ .

$f (- 1) = 2 + 3 + {(- 1)}^{4}$

Raise $- 1$ to the power of $4$ .

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

Simplify by adding numbers.

Add $2$ and $3$ .

$f (- 1) = 5 + 1$

Add $5$ and $1$ .

$f (- 1) = 6$

The final answer is $6$ .

$6$

Convert $6$ to decimal.

$y = 6$

Find the point at $x = 0$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $3$ by $0$ .

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

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

$f (0) = 2 + 0 - 0$

Multiply $- 1$ by $0$ .

$f (0) = 2 + 0 + 0$

Simplify by adding numbers.

Add $2$ and $0$ .

$f (0) = 2 + 0$

Add $2$ and $0$ .

$f (0) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify each term.

One to any power is one.

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

Multiply $3$ by $1$ .

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

One to any power is one.

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

Multiply $- 1$ by $1$ .

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

Simplify by adding and subtracting.

Add $2$ and $3$ .

$f (1) = 5 - 1$

Subtract $1$ from $5$ .

$f (1) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $3$ by $4$ .

$f (2) = 2 + 12 - {(2)}^{3}$

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

$f (2) = 2 + 12 - 1 \cdot 8$

Multiply $- 1$ by $8$ .

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

Simplify by adding and subtracting.

Add $2$ and $12$ .

$f (2) = 14 - 8$

Subtract $8$ from $14$ .

$f (2) = 6$

The final answer is $6$ .

$6$

Convert $6$ to decimal.

$y = 6$

Find the point at $x = 3$ .

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

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

Simplify the result.

Simplify each term.

Multiply $3$ by ${(3)}^{2}$ by adding the exponents.

Multiply $3$ by ${(3)}^{2}$ .

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

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

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

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

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

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

$f (3) = 2 + 27 - 1 \cdot 27$

Multiply $- 1$ by $27$ .

$f (3) = 2 + 27 - 27$

Simplify by adding and subtracting.

Add $2$ and $27$ .

$f (3) = 29 - 27$

Subtract $27$ from $29$ .

$f (3) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

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

$\begin{array}{c} x & y \\ - 1 & 6 \\ 0 & 2 \\ 1 & 4 \\ 2 & 6 \\ 3 & 2 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 1 & 6 \\ 0 & 2 \\ 1 & 4 \\ 2 & 6 \\ 3 & 2 \end{array}$

Graph c(x)=2+3x^2-x^3

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