Algebra Examples

$k (x) = {(x - 1)}^{2} - 4$

Step 1

Write $k (x) = {(x - 1)}^{2} - 4$ as an equation.

$y = {(x - 1)}^{2} - 4$

Step 2

Simplify ${(x - 1)}^{2} - 4$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$y = (x - 1) (x - 1) - 4$

Step 2.1.2

Expand $(x - 1) (x - 1)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

$y = x (x - 1) - 1 (x - 1) - 4$

Step 2.1.2.2

Apply the distributive property.

$y = x \cdot x + x \cdot - 1 - 1 (x - 1) - 4$

Step 2.1.2.3

Apply the distributive property.

$y = x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1 - 4$

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1 - 4$

Step 2.1.3.1.2

Move $- 1$ to the left of $x$ .

$y = x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1 - 4$

Step 2.1.3.1.3

Rewrite $- 1 x$ as $- x$ .

$y = x^{2} - x - 1 x - 1 \cdot - 1 - 4$

Step 2.1.3.1.4

Rewrite $- 1 x$ as $- x$ .

$y = x^{2} - x - x - 1 \cdot - 1 - 4$

Step 2.1.3.1.5

Multiply $- 1$ by $- 1$ .

$y = x^{2} - x - x + 1 - 4$

Step 2.1.3.2

Subtract $x$ from $- x$ .

$y = x^{2} - 2 x + 1 - 4$

Step 2.2

Subtract $4$ from $1$ .

$y = x^{2} - 2 x - 3$

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = 0^{2} - 2 \cdot 0 - 3$

Step 4.2

Remove parentheses.

$y = {(0)}^{2} - 2 \cdot 0 - 3$

Step 4.3

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

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

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

$y = 0 - 2 \cdot 0 - 3$

Step 4.3.1.2

Multiply $- 2$ by $0$ .

$y = 0 + 0 - 3$

Step 4.3.2

Simplify by adding and subtracting.

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Step 4.3.2.1

Add $0$ and $0$ .

$y = 0 - 3$

Step 4.3.2.2

Subtract $3$ from $0$ .

$y = - 3$

Step 4.4

Use the $x$ and $y$ values to form the ordered pair.

$(0, - 3)$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = 1^{2} - 2 \cdot 1 - 3$

Step 5.2

Remove parentheses.

$y = {(1)}^{2} - 2 \cdot 1 - 3$

Step 5.3

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

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

One to any power is one.

$y = 1 - 2 \cdot 1 - 3$

Step 5.3.1.2

Multiply $- 2$ by $1$ .

$y = 1 - 2 - 3$

Step 5.3.2

Simplify by subtracting numbers.

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Step 5.3.2.1

Subtract $2$ from $1$ .

$y = - 1 - 3$

Step 5.3.2.2

Subtract $3$ from $- 1$ .

$y = - 4$

Step 5.4

Use the $x$ and $y$ values to form the ordered pair.

$(1, - 4)$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 6.1

Remove parentheses.

$y = 2^{2} - 2 \cdot 2 - 3$

Step 6.2

Remove parentheses.

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

Step 6.3

Simplify ${(2)}^{2} - 2 \cdot 2 - 3$ .

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Step 6.3.1

Simplify each term.

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Step 6.3.1.1

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

$y = 4 - 2 \cdot 2 - 3$

Step 6.3.1.2

Multiply $- 2$ by $2$ .

$y = 4 - 4 - 3$

Step 6.3.2

Simplify by subtracting numbers.

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Step 6.3.2.1

Subtract $4$ from $4$ .

$y = 0 - 3$

Step 6.3.2.2

Subtract $3$ from $0$ .

$y = - 3$

Step 6.4

Use the $x$ and $y$ values to form the ordered pair.

$(2, - 3)$

Step 7

These are three possible solutions to the equation.

$(0, - 3), (1, - 4), (2, - 3)$

Step 8