Graph P(x)=x^3+2x^2-5x-6

$P (x) = x^{3} + 2 x^{2} - 5 x - 6$

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

$f (- 2) = - 8 + 2 \cdot 4 - 5 \cdot - 2 - 6$

Multiply $2$ by $4$ .

$f (- 2) = - 8 + 8 - 5 \cdot - 2 - 6$

Multiply $- 5$ by $- 2$ .

$f (- 2) = - 8 + 8 + 10 - 6$

Simplify by adding and subtracting.

Add $- 8$ and $8$ .

$f (- 2) = 0 + 10 - 6$

Add $0$ and $10$ .

$f (- 2) = 10 - 6$

Subtract $6$ from $10$ .

$f (- 2) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

$f (- 1) = - 1 + 2 \cdot 1 - 5 \cdot - 1 - 6$

Multiply $2$ by $1$ .

$f (- 1) = - 1 + 2 - 5 \cdot - 1 - 6$

Multiply $- 5$ by $- 1$ .

$f (- 1) = - 1 + 2 + 5 - 6$

Simplify by adding and subtracting.

Add $- 1$ and $2$ .

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

Add $1$ and $5$ .

$f (- 1) = 6 - 6$

Subtract $6$ from $6$ .

$f (- 1) = 0$

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.

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

Simplify the result.

Simplify each term.

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

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

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

$f (0) = 0 + 2 \cdot 0 - 5 \cdot 0 - 6$

Multiply $2$ by $0$ .

$f (0) = 0 + 0 - 5 \cdot 0 - 6$

Multiply $- 5$ 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.

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

Simplify the result.

Simplify each term.

One to any power is one.

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

One to any power is one.

$f (1) = 1 + 2 \cdot 1 - 5 \cdot 1 - 6$

Multiply $2$ by $1$ .

$f (1) = 1 + 2 - 5 \cdot 1 - 6$

Multiply $- 5$ by $1$ .

$f (1) = 1 + 2 - 5 - 6$

Simplify by adding and subtracting.

Add $1$ and $2$ .

$f (1) = 3 - 5 - 6$

Subtract $5$ from $3$ .

$f (1) = - 2 - 6$

Subtract $6$ from $- 2$ .

$f (1) = - 8$

The final answer is $- 8$ .

$- 8$

Convert $- 8$ to decimal.

$y = - 8$

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

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

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

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

$f (2) = 8 + 2^{1 + 2} - 5 \cdot 2 - 6$

Add $1$ and $2$ .

$f (2) = 8 + 2^{3} - 5 \cdot 2 - 6$

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

$f (2) = 8 + 8 - 5 \cdot 2 - 6$

Multiply $- 5$ by $2$ .

$f (2) = 8 + 8 - 10 - 6$

Simplify by adding and subtracting.

Add $8$ and $8$ .

$f (2) = 16 - 10 - 6$

Subtract $10$ from $16$ .

$f (2) = 6 - 6$

Subtract $6$ from $6$ .

$f (2) = 0$

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.

$\begin{array}{c} x & y \\ - 2 & 4 \\ - 1 & 0 \\ 0 & - 6 \\ 1 & - 8 \\ 2 & 0 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 2 & 4 \\ - 1 & 0 \\ 0 & - 6 \\ 1 & - 8 \\ 2 & 0 \end{array}$

Graph P(x)=x^3+2x^2-5x-6

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