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

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

Step 1

Find the point at $x = - 2$ .

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

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

Simplify the result.

Remove parentheses.

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

Simplify each term.

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

$f (- 2) = 8 - 2 {(- 2)}^{2} - 2 + 3$

Multiply $- 1$ by $- 8$ .

$f (- 2) = 8 - 2 {(- 2)}^{2} - 2 + 3$

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

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

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

$f (- 2) = 8 + (- 2) {(- 2)}^{2} - 2 + 3$

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

$f (- 2) = 8 + {(- 2)}^{1 + 2} - 2 + 3$

Add $1$ and $2$ .

$f (- 2) = 8 + {(- 2)}^{3} - 2 + 3$

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

$f (- 2) = 8 - 8 - 2 + 3$

Simplify by adding and subtracting.

Subtract $8$ from $8$ .

$f (- 2) = 0 - 2 + 3$

Subtract $2$ from $0$ .

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

Add $- 2$ and $3$ .

$f (- 2) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Step 2

Find the point at $x = 0$ .

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

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

Simplify the result.

Remove parentheses.

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

Simplify each term.

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

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

Multiply $- 1$ by $0$ .

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

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

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

Multiply $- 2$ by $0$ .

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

Simplify by adding numbers.

Add $0$ and $0$ .

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

Add $0$ and $0$ .

$f (0) = 0 + 3$

Add $0$ and $3$ .

$f (0) = 3$

The final answer is $3$ .

$3$

Convert $3$ to decimal.

$y = 3$

Step 3

Find the point at $x = 1$ .

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

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

Simplify the result.

Remove parentheses.

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

Simplify each term.

One to any power is one.

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

Multiply $- 1$ by $1$ .

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

One to any power is one.

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

Multiply $- 2$ by $1$ .

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

Simplify by adding and subtracting.

Subtract $2$ from $- 1$ .

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

Add $- 3$ and $1$ .

$f (1) = - 2 + 3$

Add $- 2$ and $3$ .

$f (1) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Step 4

Find the point at $x = 2$ .

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

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

Simplify the result.

Remove parentheses.

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

Simplify each term.

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

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

Multiply $- 1$ by $8$ .

$f (2) = - 8 - 2 {(2)}^{2} + 2 + 3$

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

$f (2) = - 8 - 2 \cdot 4 + 2 + 3$

Multiply $- 2$ by $4$ .

$f (2) = - 8 - 8 + 2 + 3$

Simplify by adding and subtracting.

Subtract $8$ from $- 8$ .

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

Add $- 16$ and $2$ .

$f (2) = - 14 + 3$

Add $- 14$ and $3$ .

$f (2) = - 11$

The final answer is $- 11$ .

$- 11$

Convert $- 11$ to decimal.

$y = - 11$

Step 5

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

$\begin{array}{c} x & y \\ - 2 & 1 \\ - 1 & 1 \\ 0 & 3 \\ 1 & 1 \\ 2 & - 11 \end{array}$

Step 6

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 2 & 1 \\ - 1 & 1 \\ 0 & 3 \\ 1 & 1 \\ 2 & - 11 \end{array}$

Step 7

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

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