Graph h(p)=6p-p^3-2

$h (p) = 6 p - p^{3} - 2$

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

Multiply $6$ by $- 2$ .

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

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

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

Multiply $- 1$ by $- 8$ .

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

Simplify by adding and subtracting.

Add $- 12$ and $8$ .

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

Subtract $2$ from $- 4$ .

$f (- 2) = - 6$

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.

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

Simplify the result.

Simplify each term.

Multiply $6$ by $- 1$ .

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

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

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

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

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

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

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

Add $1$ and $3$ .

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

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

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

Simplify by adding and subtracting.

Add $- 6$ and $1$ .

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

Subtract $2$ from $- 5$ .

$f (- 1) = - 7$

The final answer is $- 7$ .

$- 7$

Convert $- 7$ to decimal.

$y = - 7$

Find the point at $x = 0$ .

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

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

Simplify the result.

Simplify each term.

Multiply $6$ by $0$ .

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

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

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

Multiply $- 1$ by $0$ .

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

Simplify by adding and subtracting.

Add $0$ and $0$ .

$f (0) = 0 - 2$

Subtract $2$ from $0$ .

$f (0) = - 2$

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.

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

Simplify the result.

Simplify each term.

Multiply $6$ by $1$ .

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

One to any power is one.

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

Multiply $- 1$ by $1$ .

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

Simplify by subtracting numbers.

Subtract $1$ from $6$ .

$f (1) = 5 - 2$

Subtract $2$ from $5$ .

$f (1) = 3$

The final answer is $3$ .

$3$

Convert $3$ to decimal.

$y = 3$

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

Multiply $6$ by $2$ .

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

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

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

Multiply $- 1$ by $8$ .

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

Simplify by subtracting numbers.

Subtract $8$ from $12$ .

$f (2) = 4 - 2$

Subtract $2$ from $4$ .

$f (2) = 2$

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.

$\begin{array}{c} x & y \\ - 2 & - 6 \\ - 1 & - 7 \\ 0 & - 2 \\ 1 & 3 \\ 2 & 2 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 2 & - 6 \\ - 1 & - 7 \\ 0 & - 2 \\ 1 & 3 \\ 2 & 2 \end{array}$

Graph h(p)=6p-p^3-2

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