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

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

Step 1

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

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

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.

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

Remove parentheses.

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

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

Simplify each term.

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

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

Multiply $5$ by $0$ .

$y = 0 + 0 + 6$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 6$

Add $0$ and $6$ .

$y = 6$

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

$(0, 6)$

Step 4

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

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

One to any power is one.

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

Multiply $5$ by $1$ .

$y = 1 + 5 + 6$

Simplify by adding numbers.

Add $1$ and $5$ .

$y = 6 + 6$

Add $6$ and $6$ .

$y = 12$

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

$(1, 12)$

Step 5

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

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

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

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

Multiply $5$ by $2$ .

$y = 4 + 10 + 6$

Simplify by adding numbers.

Add $4$ and $10$ .

$y = 14 + 6$

Add $14$ and $6$ .

$y = 20$

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

$(2, 20)$

Step 6

These are three possible solutions to the equation.

$(0, 6), (1, 12), (2, 20)$

Step 7

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

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