Find Three Ordered Pair Solutions a(x)=-(x+3)^2-2

$a (x) = - {(x + 3)}^{2} - 2$

Step 1

Write $a (x) = - {(x + 3)}^{2} - 2$ as an equation.

$y = - {(x + 3)}^{2} - 2$

Step 2

Simplify $- {(x + 3)}^{2} - 2$ .

Simplify each term.

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$y = - ((x + 3) (x + 3)) - 2$

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$y = - (x (x + 3) + 3 (x + 3)) - 2$

Apply the distributive property.

$y = - (x \cdot x + x \cdot 3 + 3 (x + 3)) - 2$

Apply the distributive property.

$y = - (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) - 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $3$ to the left of $x$ .

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

Multiply $3$ by $3$ .

$y = - (x^{2} + 3 x + 3 x + 9) - 2$

Add $3 x$ and $3 x$ .

$y = - (x^{2} + 6 x + 9) - 2$

Apply the distributive property.

$y = - x^{2} - (6 x) - 1 \cdot 9 - 2$

Simplify.

Multiply $6$ by $- 1$ .

$y = - x^{2} - 6 x - 1 \cdot 9 - 2$

Multiply $- 1$ by $9$ .

$y = - x^{2} - 6 x - 9 - 2$

Subtract $2$ from $- 9$ .

$y = - x^{2} - 6 x - 11$

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.

$y = - 0^{2} - 6 \cdot 0 - 11$

Remove parentheses.

$y = - {(0)}^{2} - 6 \cdot 0 - 11$

Simplify $- {(0)}^{2} - 6 \cdot 0 - 11$ .

Simplify each term.

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

$y = - 0 - 6 \cdot 0 - 11$

Multiply $- 1$ by $0$ .

$y = 0 - 6 \cdot 0 - 11$

Multiply $- 6$ by $0$ .

$y = 0 + 0 - 11$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 11$

Subtract $11$ from $0$ .

$y = - 11$

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

$(0, - 11)$

Step 5

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

Remove parentheses.

$y = - 1^{2} - 6 \cdot 1 - 11$

Remove parentheses.

$y = - {(1)}^{2} - 6 \cdot 1 - 11$

Simplify $- {(1)}^{2} - 6 \cdot 1 - 11$ .

Simplify each term.

One to any power is one.

$y = - 1 \cdot 1 - 6 \cdot 1 - 11$

Multiply $- 1$ by $1$ .

$y = - 1 - 6 \cdot 1 - 11$

Multiply $- 6$ by $1$ .

$y = - 1 - 6 - 11$

Simplify by subtracting numbers.

Subtract $6$ from $- 1$ .

$y = - 7 - 11$

Subtract $11$ from $- 7$ .

$y = - 18$

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

$(1, - 18)$

Step 6

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

Remove parentheses.

$y = - 2^{2} - 6 \cdot 2 - 11$

Remove parentheses.

$y = - {(2)}^{2} - 6 \cdot 2 - 11$

Simplify $- {(2)}^{2} - 6 \cdot 2 - 11$ .

Simplify each term.

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

$y = - 1 \cdot 4 - 6 \cdot 2 - 11$

Multiply $- 1$ by $4$ .

$y = - 4 - 6 \cdot 2 - 11$

Multiply $- 6$ by $2$ .

$y = - 4 - 12 - 11$

Simplify by subtracting numbers.

Subtract $12$ from $- 4$ .

$y = - 16 - 11$

Subtract $11$ from $- 16$ .

$y = - 27$

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

$(2, - 27)$

Step 7

These are three possible solutions to the equation.

$(0, - 11), (1, - 18), (2, - 27)$

Step 8

Find Three Ordered Pair Solutions a(x)=-(x+3)^2-2

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