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

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

Step 1

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

$f (- 2) = - 8 + 4 + 2$

Simplify by adding numbers.

Add $- 8$ and $4$ .

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

Add $- 4$ and $2$ .

$f (- 2) = - 2$

The final answer is $- 2$ .

$- 2$

Convert $- 2$ to decimal.

$y = - 2$

Step 2

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

Simplify by adding numbers.

Add $- 1$ and $1$ .

$f (- 1) = 0 + 2$

Add $0$ and $2$ .

$f (- 1) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Step 3

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify each term.

One to any power is one.

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

One to any power is one.

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

Simplify by adding numbers.

Add $1$ and $1$ .

$f (1) = 2 + 2$

Add $2$ and $2$ .

$f (1) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Step 4

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

$f (2) = 8 + 4 + 2$

Simplify by adding numbers.

Add $8$ and $4$ .

$f (2) = 12 + 2$

Add $12$ and $2$ .

$f (2) = 14$

The final answer is $14$ .

$14$

Convert $14$ to decimal.

$y = 14$

Step 5

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

$\begin{array}{c} x & y \\ - 2 & - 2 \\ - 1 & 2 \\ 0 & 2 \\ 1 & 4 \\ 2 & 14 \end{array}$

Step 6

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 2 & - 2 \\ - 1 & 2 \\ 0 & 2 \\ 1 & 4 \\ 2 & 14 \end{array}$

Step 7

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

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