Graph f(x)=2x^3-4x^2+x+1

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

Find the point at $x = - 1$ .

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

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

Simplify the result.

Remove parentheses.

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

Simplify each term.

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

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

Multiply $2$ by $- 1$ .

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

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

$f (- 1) = - 2 - 4 \cdot 1 - 1 + 1$

Multiply $- 4$ by $1$ .

$f (- 1) = - 2 - 4 - 1 + 1$

Simplify by adding and subtracting.

Subtract $4$ from $- 2$ .

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

Subtract $1$ from $- 6$ .

$f (- 1) = - 7 + 1$

Add $- 7$ 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.

$f (0) = 2 {(0)}^{3} - 4 {(0)}^{2} + 0 + 1$

Simplify the result.

Remove parentheses.

$f (0) = 2 {(0)}^{3} - 4 {(0)}^{2} + 0 + 1$

Simplify each term.

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

$f (0) = 2 \cdot 0 - 4 {(0)}^{2} + 0 + 1$

Multiply $2$ by $0$ .

$f (0) = 0 - 4 {(0)}^{2} + 0 + 1$

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

$f (0) = 0 - 4 \cdot 0 + 0 + 1$

Multiply $- 4$ by $0$ .

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

Simplify by adding numbers.

Add $0$ and $0$ .

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

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.

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

Simplify the result.

Remove parentheses.

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

Simplify each term.

One to any power is one.

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

Multiply $2$ by $1$ .

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

One to any power is one.

$f (1) = 2 - 4 \cdot 1 + 1 + 1$

Multiply $- 4$ by $1$ .

$f (1) = 2 - 4 + 1 + 1$

Simplify by adding and subtracting.

Subtract $4$ from $2$ .

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

Add $- 2$ and $1$ .

$f (1) = - 1 + 1$

Add $- 1$ and $1$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 2$ .

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

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

Simplify the result.

Remove parentheses.

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

Simplify each term.

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

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

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

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

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

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

Add $1$ and $3$ .

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

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

$f (2) = 16 - 4 {(2)}^{2} + 2 + 1$

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

$f (2) = 16 - 4 \cdot 4 + 2 + 1$

Multiply $- 4$ by $4$ .

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

Simplify by adding and subtracting.

Subtract $16$ from $16$ .

$f (2) = 0 + 2 + 1$

Add $0$ and $2$ .

$f (2) = 2 + 1$

Add $2$ and $1$ .

$f (2) = 3$

The final answer is $3$ .

$3$

Convert $3$ to decimal.

$y = 3$

Find the point at $x = 3$ .

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

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

Simplify the result.

Remove parentheses.

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

Simplify each term.

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

$f (3) = 2 \cdot 27 - 4 {(3)}^{2} + 3 + 1$

Multiply $2$ by $27$ .

$f (3) = 54 - 4 {(3)}^{2} + 3 + 1$

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

$f (3) = 54 - 4 \cdot 9 + 3 + 1$

Multiply $- 4$ by $9$ .

$f (3) = 54 - 36 + 3 + 1$

Simplify by adding and subtracting.

Subtract $36$ from $54$ .

$f (3) = 18 + 3 + 1$

Add $18$ and $3$ .

$f (3) = 21 + 1$

Add $21$ and $1$ .

$f (3) = 22$

The final answer is $22$ .

$22$

Convert $22$ to decimal.

$y = 22$

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

$\begin{array}{c} x & y \\ - 1 & - 6 \\ 0 & 1 \\ 1 & 0 \\ 2 & 3 \\ 3 & 22 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 1 & - 6 \\ 0 & 1 \\ 1 & 0 \\ 2 & 3 \\ 3 & 22 \end{array}$

Graph f(x)=2x^3-4x^2+x+1

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