Find Three Ordered Pair Solutions r(x)=-x^2+6x-5

$r (x) = - x^{2} + 6 x - 5$

Step 1

Write $r (x) = - x^{2} + 6 x - 5$ as an equation.

$y = - x^{2} + 6 x - 5$

Step 2

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

Step 3

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

Remove parentheses.

$y = - 0^{2} + 6 (0) - 5$

Remove parentheses.

$y = - {(0)}^{2} + 6 (0) - 5$

Simplify $- {(0)}^{2} + 6 (0) - 5$ .

Simplify each term.

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

$y = - 0 + 6 (0) - 5$

Multiply $- 1$ by $0$ .

$y = 0 + 6 (0) - 5$

Multiply $6$ 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 4

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

Remove parentheses.

$y = - 1^{2} + 6 (1) - 5$

Remove parentheses.

$y = - {(1)}^{2} + 6 (1) - 5$

Simplify $- {(1)}^{2} + 6 (1) - 5$ .

Simplify each term.

One to any power is one.

$y = - 1 \cdot 1 + 6 (1) - 5$

Multiply $- 1$ by $1$ .

$y = - 1 + 6 (1) - 5$

Multiply $6$ by $1$ .

$y = - 1 + 6 - 5$

Simplify by adding and subtracting.

Add $- 1$ and $6$ .

$y = 5 - 5$

Subtract $5$ from $5$ .

$y = 0$

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

$(1, 0)$

Step 5

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

Remove parentheses.

$y = - 2^{2} + 6 (2) - 5$

Remove parentheses.

$y = - {(2)}^{2} + 6 (2) - 5$

Simplify $- {(2)}^{2} + 6 (2) - 5$ .

Simplify each term.

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

$y = - 1 \cdot 4 + 6 (2) - 5$

Multiply $- 1$ by $4$ .

$y = - 4 + 6 (2) - 5$

Multiply $6$ by $2$ .

$y = - 4 + 12 - 5$

Simplify by adding and subtracting.

Add $- 4$ and $12$ .

$y = 8 - 5$

Subtract $5$ from $8$ .

$y = 3$

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

$(2, 3)$

Step 6

These are three possible solutions to the equation.

$(0, - 5), (1, 0), (2, 3)$

Step 7

Find Three Ordered Pair Solutions r(x)=-x^2+6x-5

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