Find Three Ordered Pair Solutions k(x)=(x-1)^2-6

$k (x) = {(x - 1)}^{2} - 6$

Step 1

Write $k (x) = {(x - 1)}^{2} - 6$ as an equation.

$y = {(x - 1)}^{2} - 6$

Step 2

Simplify ${(x - 1)}^{2} - 6$ .

Simplify each term.

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

$y = (x - 1) (x - 1) - 6$

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

Apply the distributive property.

$y = x (x - 1) - 1 (x - 1) - 6$

Apply the distributive property.

$y = x \cdot x + x \cdot - 1 - 1 (x - 1) - 6$

Apply the distributive property.

$y = x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1 - 6$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1 - 6$

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

$y = x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1 - 6$

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

$y = x^{2} - x - 1 x - 1 \cdot - 1 - 6$

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

$y = x^{2} - x - x - 1 \cdot - 1 - 6$

Multiply $- 1$ by $- 1$ .

$y = x^{2} - x - x + 1 - 6$

Subtract $x$ from $- x$ .

$y = x^{2} - 2 x + 1 - 6$

Subtract $6$ from $1$ .

$y = x^{2} - 2 x - 5$

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.

Remove parentheses.

$y = 0^{2} - 2 \cdot 0 - 5$

Remove parentheses.

$y = {(0)}^{2} - 2 \cdot 0 - 5$

Simplify ${(0)}^{2} - 2 \cdot 0 - 5$ .

Simplify each term.

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

$y = 0 - 2 \cdot 0 - 5$

Multiply $- 2$ by $0$ .

$y = 0 + 0 - 5$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 5$

Subtract $5$ from $0$ .

$y = - 5$

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

$(0, - 5)$

Step 5

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

Remove parentheses.

$y = 1^{2} - 2 \cdot 1 - 5$

Remove parentheses.

$y = {(1)}^{2} - 2 \cdot 1 - 5$

Simplify ${(1)}^{2} - 2 \cdot 1 - 5$ .

Simplify each term.

One to any power is one.

$y = 1 - 2 \cdot 1 - 5$

Multiply $- 2$ by $1$ .

$y = 1 - 2 - 5$

Simplify by subtracting numbers.

Subtract $2$ from $1$ .

$y = - 1 - 5$

Subtract $5$ from $- 1$ .

$y = - 6$

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

$(1, - 6)$

Step 6

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

Remove parentheses.

$y = 2^{2} - 2 \cdot 2 - 5$

Remove parentheses.

$y = {(2)}^{2} - 2 \cdot 2 - 5$

Simplify ${(2)}^{2} - 2 \cdot 2 - 5$ .

Simplify each term.

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

$y = 4 - 2 \cdot 2 - 5$

Multiply $- 2$ by $2$ .

$y = 4 - 4 - 5$

Simplify by subtracting numbers.

Subtract $4$ from $4$ .

$y = 0 - 5$

Subtract $5$ from $0$ .

$y = - 5$

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

$(2, - 5)$

Step 7

These are three possible solutions to the equation.

$(0, - 5), (1, - 6), (2, - 5)$

Step 8

Find Three Ordered Pair Solutions k(x)=(x-1)^2-6

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