Graph y=-2x^3+3x+1

$y = - 2 x^{3} + 3 x + 1$

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $3$ .

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

Raise $- 2$ to the power of $4$ .

$f (- 2) = 16 + 3 (- 2) + 1$

Multiply $3$ by $- 2$ .

$f (- 2) = 16 - 6 + 1$

Simplify by adding and subtracting.

Subtract $6$ from $16$ .

$f (- 2) = 10 + 1$

Add $10$ and $1$ .

$f (- 2) = 11$

The final answer is $11$ .

$11$

Convert $11$ to decimal.

$y = 11$

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 2$ by $- 1$ .

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

Multiply $3$ by $- 1$ .

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

Simplify by adding and subtracting.

Subtract $3$ from $2$ .

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

Add $- 1$ and $1$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 0$ .

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

$f (0) = - 2 {(0)}^{3} + 3 (0) + 1$

Simplify the result.

Simplify each term.

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

$f (0) = - 2 \cdot 0 + 3 (0) + 1$

Multiply $- 2$ by $0$ .

$f (0) = 0 + 3 (0) + 1$

Multiply $3$ by $0$ .

$f (0) = 0 + 0 + 1$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 1$

Add $0$ and $1$ .

$f (0) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify each term.

One to any power is one.

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

Multiply $- 2$ by $1$ .

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

Multiply $3$ by $1$ .

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

Simplify by adding numbers.

Add $- 2$ and $3$ .

$f (1) = 1 + 1$

Add $1$ and $1$ .

$f (1) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

$f (2) = - 2 \cdot 8 + 3 (2) + 1$

Multiply $- 2$ by $8$ .

$f (2) = - 16 + 3 (2) + 1$

Multiply $3$ by $2$ .

$f (2) = - 16 + 6 + 1$

Simplify by adding numbers.

Add $- 16$ and $6$ .

$f (2) = - 10 + 1$

Add $- 10$ and $1$ .

$f (2) = - 9$

The final answer is $- 9$ .

$- 9$

Convert $- 9$ to decimal.

$y = - 9$

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

$\begin{array}{c} x & y \\ - 2 & 11 \\ - 1 & 0 \\ 0 & 1 \\ 1 & 2 \\ 2 & - 9 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 2 & 11 \\ - 1 & 0 \\ 0 & 1 \\ 1 & 2 \\ 2 & - 9 \end{array}$

Graph y=-2x^3+3x+1

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