Algebra Examples

$y = x^{2} - 2 x$

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

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

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

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

$y = 4 - 2 \cdot - 2$

Step 2.2.1.2

Multiply $- 2$ by $- 2$ .

$y = 4 + 4$

Step 2.2.2

Add $4$ and $4$ .

$y = 8$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

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

Step 4.2

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

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

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

$y = 1 - 2 \cdot - 1$

Step 4.2.1.2

Multiply $- 2$ by $- 1$ .

$y = 1 + 2$

Step 4.2.2

Add $1$ and $2$ .

$y = 3$

Step 5

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

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = 0^{2} - 2 \cdot 0$

Step 6.2

Remove parentheses.

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

Step 6.3

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

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Step 6.3.1

Simplify each term.

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Step 6.3.1.1

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

$y = 0 - 2 \cdot 0$

Step 6.3.1.2

Multiply $- 2$ by $0$ .

$y = 0 + 0$

Step 6.3.2

Add $0$ and $0$ .

$y = 0$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = 1^{2} - 2 \cdot 1$

Step 8.2

Remove parentheses.

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

Step 8.3

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

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Step 8.3.1

Simplify each term.

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Step 8.3.1.1

One to any power is one.

$y = 1 - 2 \cdot 1$

Step 8.3.1.2

Multiply $- 2$ by $1$ .

$y = 1 - 2$

Step 8.3.2

Subtract $2$ from $1$ .

$y = - 1$

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = 2^{2} - 2 \cdot 2$

Step 10.2

Remove parentheses.

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

Step 10.3

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

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Step 10.3.1

Simplify each term.

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Step 10.3.1.1

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

$y = 4 - 2 \cdot 2$

Step 10.3.1.2

Multiply $- 2$ by $2$ .

$y = 4 - 4$

Step 10.3.2

Subtract $4$ from $4$ .

$y = 0$

Step 11

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

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

Step 12