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

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $2$ from $- 2$ .

$y = {(- 4)}^{2}$

Raise $- 4$ to the power of $2$ .

$y = 16$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $2$ from $- 1$ .

$y = {(- 3)}^{2}$

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

$y = 9$

Step 5

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

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $2$ from $0$ .

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

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

$y = 4$

Step 7

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

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $2$ from $1$ .

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

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

$y = 1$

Step 9

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

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $2$ from $2$ .

$y = 0^{2}$

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

$y = 0$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 16 \\ - 1 & 9 \\ 0 & 4 \\ 1 & 1 \\ 2 & 0 \end{array}$

Step 12

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

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