Algebra Examples

$Y = x^{2} + 2 x - 3$

Step 1

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

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

Step 2

Simplify ${(- 2)}^{2} + 2 (- 2) - 3$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$Y = 4 + 2 (- 2) - 3$

Step 2.1.2

Multiply $2$ by $- 2$ .

$Y = 4 - 4 - 3$

Step 2.2

Simplify by subtracting numbers.

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Step 2.2.1

Subtract $4$ from $4$ .

$Y = 0 - 3$

Step 2.2.2

Subtract $3$ from $0$ .

$Y = - 3$

Step 3

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

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

Step 4

Simplify ${(- 1)}^{2} + 2 (- 1) - 3$ .

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Step 4.1

Simplify each term.

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Step 4.1.1

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

$Y = 1 + 2 (- 1) - 3$

Step 4.1.2

Multiply $2$ by $- 1$ .

$Y = 1 - 2 - 3$

Step 4.2

Simplify by subtracting numbers.

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Step 4.2.1

Subtract $2$ from $1$ .

$Y = - 1 - 3$

Step 4.2.2

Subtract $3$ from $- 1$ .

$Y = - 4$

Step 5

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

$Y = {(0)}^{2} + 2 (0) - 3$

Step 6

Simplify ${(0)}^{2} + 2 (0) - 3$ .

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Step 6.1

Simplify each term.

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Step 6.1.1

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

$Y = 0 + 2 (0) - 3$

Step 6.1.2

Multiply $2$ by $0$ .

$Y = 0 + 0 - 3$

Step 6.2

Simplify by adding and subtracting.

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Step 6.2.1

Add $0$ and $0$ .

$Y = 0 - 3$

Step 6.2.2

Subtract $3$ from $0$ .

$Y = - 3$

Step 7

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

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

Step 8

Simplify ${(1)}^{2} + 2 (1) - 3$ .

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Step 8.1

Simplify each term.

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Step 8.1.1

One to any power is one.

$Y = 1 + 2 (1) - 3$

Step 8.1.2

Multiply $2$ by $1$ .

$Y = 1 + 2 - 3$

Step 8.2

Simplify by adding and subtracting.

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Step 8.2.1

Add $1$ and $2$ .

$Y = 3 - 3$

Step 8.2.2

Subtract $3$ from $3$ .

$Y = 0$

Step 9

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

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

Step 10

Simplify ${(2)}^{2} + 2 (2) - 3$ .

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Step 10.1

Simplify each term.

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Step 10.1.1

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

$Y = 4 + 2 (2) - 3$

Step 10.1.2

Multiply $2$ by $2$ .

$Y = 4 + 4 - 3$

Step 10.2

Simplify by adding and subtracting.

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Step 10.2.1

Add $4$ and $4$ .

$Y = 8 - 3$

Step 10.2.2

Subtract $3$ from $8$ .

$Y = 5$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 3 \\ - 1 & - 4 \\ 0 & - 3 \\ 1 & 0 \\ 2 & 5 \end{array}$

Step 12