Find Three Ordered Pair Solutions t(x)=(x-5)^2-2

$t (x) = {(x - 5)}^{2} - 2$

Step 1

Write $t (x) = {(x - 5)}^{2} - 2$ as an equation.

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

Step 2

Simplify ${(x - 5)}^{2} - 2$ .

Simplify each term.

Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

$y = (x - 5) (x - 5) - 2$

Expand $(x - 5) (x - 5)$ using the FOIL Method.

Apply the distributive property.

$y = x (x - 5) - 5 (x - 5) - 2$

Apply the distributive property.

$y = x \cdot x + x \cdot - 5 - 5 (x - 5) - 2$

Apply the distributive property.

$y = x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5 - 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 5$ to the left of $x$ .

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

Multiply $- 5$ by $- 5$ .

$y = x^{2} - 5 x - 5 x + 25 - 2$

Subtract $5 x$ from $- 5 x$ .

$y = x^{2} - 10 x + 25 - 2$

Subtract $2$ from $25$ .

$y = x^{2} - 10 x + 23$

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.

$y = 0^{2} - 10 \cdot 0 + 23$

Remove parentheses.

$y = {(0)}^{2} - 10 \cdot 0 + 23$

Simplify ${(0)}^{2} - 10 \cdot 0 + 23$ .

Simplify each term.

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

$y = 0 - 10 \cdot 0 + 23$

Multiply $- 10$ by $0$ .

$y = 0 + 0 + 23$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 23$

Add $0$ and $23$ .

$y = 23$

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

$(0, 23)$

Step 5

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

Remove parentheses.

$y = 1^{2} - 10 \cdot 1 + 23$

Remove parentheses.

$y = {(1)}^{2} - 10 \cdot 1 + 23$

Simplify ${(1)}^{2} - 10 \cdot 1 + 23$ .

Simplify each term.

One to any power is one.

$y = 1 - 10 \cdot 1 + 23$

Multiply $- 10$ by $1$ .

$y = 1 - 10 + 23$

Simplify by adding and subtracting.

Subtract $10$ from $1$ .

$y = - 9 + 23$

Add $- 9$ and $23$ .

$y = 14$

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

$(1, 14)$

Step 6

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

Remove parentheses.

$y = 2^{2} - 10 \cdot 2 + 23$

Remove parentheses.

$y = {(2)}^{2} - 10 \cdot 2 + 23$

Simplify ${(2)}^{2} - 10 \cdot 2 + 23$ .

Simplify each term.

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

$y = 4 - 10 \cdot 2 + 23$

Multiply $- 10$ by $2$ .

$y = 4 - 20 + 23$

Simplify by adding and subtracting.

Subtract $20$ from $4$ .

$y = - 16 + 23$

Add $- 16$ and $23$ .

$y = 7$

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

$(2, 7)$

Step 7

These are three possible solutions to the equation.

$(0, 23), (1, 14), (2, 7)$

Step 8

Find Three Ordered Pair Solutions t(x)=(x-5)^2-2

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