Algebra Examples

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

Remove parentheses.

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

Step 2.3

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

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Subtract $1$ from $- 2$ .

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

Step 2.3.1.2

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

$y = 9 + 2$

Step 2.3.2

Add $9$ and $2$ .

$y = 11$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

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

Step 4.2

Remove parentheses.

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

Step 4.3

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

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Subtract $1$ from $- 1$ .

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

Step 4.3.1.2

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

$y = 4 + 2$

Step 4.3.2

Add $4$ and $2$ .

$y = 6$

Step 5

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

$y = {((0) - 1)}^{2} + 2$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = {(0 - 1)}^{2} + 2$

Step 6.2

Remove parentheses.

$y = {((0) - 1)}^{2} + 2$

Step 6.3

Simplify ${((0) - 1)}^{2} + 2$ .

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Step 6.3.1

Simplify each term.

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Step 6.3.1.1

Subtract $1$ from $0$ .

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

Step 6.3.1.2

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

$y = 1 + 2$

Step 6.3.2

Add $1$ and $2$ .

$y = 3$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

Remove parentheses.

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

Step 8.3

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

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Step 8.3.1

Simplify each term.

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Step 8.3.1.1

Subtract $1$ from $1$ .

$y = 0^{2} + 2$

Step 8.3.1.2

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

$y = 0 + 2$

Step 8.3.2

Add $0$ and $2$ .

$y = 2$

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

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

Step 10.2

Remove parentheses.

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

Step 10.3

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

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Step 10.3.1

Simplify each term.

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Step 10.3.1.1

Subtract $1$ from $2$ .

$y = 1^{2} + 2$

Step 10.3.1.2

One to any power is one.

$y = 1 + 2$

Step 10.3.2

Add $1$ and $2$ .

$y = 3$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 11 \\ - 1 & 6 \\ 0 & 3 \\ 1 & 2 \\ 2 & 3 \end{array}$

Step 12