Graph Using a Table of Values f(x)=x^2+2x

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

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = {(- 2)}^{2} + 2 (- 2)$

Step 2

Simplify ${(- 2)}^{2} + 2 (- 2)$ .

Simplify each term.

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

$y = 4 + 2 (- 2)$

Multiply $2$ by $- 2$ .

$y = 4 - 4$

Subtract $4$ from $4$ .

$y = 0$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

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

Step 4

Simplify ${(- 1)}^{2} + 2 (- 1)$ .

Simplify each term.

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

$y = 1 + 2 (- 1)$

Multiply $2$ by $- 1$ .

$y = 1 - 2$

Subtract $2$ from $1$ .

$y = - 1$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = {(0)}^{2} + 2 (0)$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = 0^{2} + 2 (0)$

Remove parentheses.

$y = {(0)}^{2} + 2 (0)$

Simplify ${(0)}^{2} + 2 (0)$ .

Simplify each term.

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

$y = 0 + 2 (0)$

Multiply $2$ by $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

Simplify ${(1)}^{2} + 2 (1)$ .

Simplify each term.

One to any power is one.

$y = 1 + 2 (1)$

Multiply $2$ by $1$ .

$y = 1 + 2$

Add $1$ and $2$ .

$y = 3$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = {(2)}^{2} + 2 (2)$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = 2^{2} + 2 (2)$

Remove parentheses.

$y = {(2)}^{2} + 2 (2)$

Simplify ${(2)}^{2} + 2 (2)$ .

Simplify each term.

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

$y = 4 + 2 (2)$

Multiply $2$ by $2$ .

$y = 4 + 4$

Add $4$ and $4$ .

$y = 8$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & - 1 \\ 0 & 0 \\ 1 & 3 \\ 2 & 8 \end{array}$

Step 12

Graph Using a Table of Values f(x)=x^2+2x

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