Graph f(x)=x^3+4x^2+x-6

$f (x) = x^{3} + 4 x^{2} + x - 6$

Find the point at $x = - 3$ .

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

$f (- 3) = {(- 3)}^{3} + 4 {(- 3)}^{2} - 3 - 6$

Simplify the result.

Remove parentheses.

$f (- 3) = {(- 3)}^{3} + 4 {(- 3)}^{2} - 3 - 6$

Simplify each term.

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

$f (- 3) = - 27 + 4 {(- 3)}^{2} - 3 - 6$

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

$f (- 3) = - 27 + 4 \cdot 9 - 3 - 6$

Multiply $4$ by $9$ .

$f (- 3) = - 27 + 36 - 3 - 6$

Simplify by adding and subtracting.

Add $- 27$ and $36$ .

$f (- 3) = 9 - 3 - 6$

Subtract $3$ from $9$ .

$f (- 3) = 6 - 6$

Subtract $6$ from $6$ .

$f (- 3) = 0$

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.

$f (- 1) = {(- 1)}^{3} + 4 {(- 1)}^{2} - 1 - 6$

Simplify the result.

Remove parentheses.

$f (- 1) = {(- 1)}^{3} + 4 {(- 1)}^{2} - 1 - 6$

Simplify each term.

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

$f (- 1) = - 1 + 4 {(- 1)}^{2} - 1 - 6$

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

$f (- 1) = - 1 + 4 \cdot 1 - 1 - 6$

Multiply $4$ by $1$ .

$f (- 1) = - 1 + 4 - 1 - 6$

Simplify by adding and subtracting.

Add $- 1$ and $4$ .

$f (- 1) = 3 - 1 - 6$

Subtract $1$ from $3$ .

$f (- 1) = 2 - 6$

Subtract $6$ from $2$ .

$f (- 1) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Find the point at $x = 0$ .

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

$f (0) = {(0)}^{3} + 4 {(0)}^{2} + 0 - 6$

Simplify the result.

Remove parentheses.

$f (0) = {(0)}^{3} + 4 {(0)}^{2} + 0 - 6$

Simplify each term.

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

$f (0) = 0 + 4 {(0)}^{2} + 0 - 6$

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

$f (0) = 0 + 4 \cdot 0 + 0 - 6$

Multiply $4$ by $0$ .

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

Simplify by adding and subtracting.

Add $0$ and $0$ .

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

Add $0$ and $0$ .

$f (0) = 0 - 6$

Subtract $6$ from $0$ .

$f (0) = - 6$

The final answer is $- 6$ .

$- 6$

Convert $- 6$ to decimal.

$y = - 6$

Find the point at $x = 1$ .

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

$f (1) = {(1)}^{3} + 4 {(1)}^{2} + 1 - 6$

Simplify the result.

Remove parentheses.

$f (1) = {(1)}^{3} + 4 {(1)}^{2} + 1 - 6$

Simplify each term.

One to any power is one.

$f (1) = 1 + 4 {(1)}^{2} + 1 - 6$

One to any power is one.

$f (1) = 1 + 4 \cdot 1 + 1 - 6$

Multiply $4$ by $1$ .

$f (1) = 1 + 4 + 1 - 6$

Simplify by adding and subtracting.

Add $1$ and $4$ .

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

Add $5$ and $1$ .

$f (1) = 6 - 6$

Subtract $6$ from $6$ .

$f (1) = 0$

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.

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

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

Falls to the left and rises to the right

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

Graph f(x)=x^3+4x^2+x-6

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