Algebra Examples

$r (x) = x^{2} + 9 x + 20$

Step 1

Write $r (x) = x^{2} + 9 x + 20$ as an equation.

$y = x^{2} + 9 x + 20$

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.

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Step 3.1

Remove parentheses.

$y = 0^{2} + 9 (0) + 20$

Step 3.2

Remove parentheses.

$y = {(0)}^{2} + 9 (0) + 20$

Step 3.3

Simplify ${(0)}^{2} + 9 (0) + 20$ .

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

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

$y = 0 + 9 (0) + 20$

Step 3.3.1.2

Multiply $9$ by $0$ .

$y = 0 + 0 + 20$

Step 3.3.2

Simplify by adding numbers.

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Step 3.3.2.1

Add $0$ and $0$ .

$y = 0 + 20$

Step 3.3.2.2

Add $0$ and $20$ .

$y = 20$

Step 3.4

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

$(0, 20)$

Step 4

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

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Step 4.1

Remove parentheses.

$y = 1^{2} + 9 (1) + 20$

Step 4.2

Remove parentheses.

$y = {(1)}^{2} + 9 (1) + 20$

Step 4.3

Simplify ${(1)}^{2} + 9 (1) + 20$ .

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

One to any power is one.

$y = 1 + 9 (1) + 20$

Step 4.3.1.2

Multiply $9$ by $1$ .

$y = 1 + 9 + 20$

Step 4.3.2

Simplify by adding numbers.

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Step 4.3.2.1

Add $1$ and $9$ .

$y = 10 + 20$

Step 4.3.2.2

Add $10$ and $20$ .

$y = 30$

Step 4.4

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

$(1, 30)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = 2^{2} + 9 (2) + 20$

Step 5.2

Remove parentheses.

$y = {(2)}^{2} + 9 (2) + 20$

Step 5.3

Simplify ${(2)}^{2} + 9 (2) + 20$ .

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

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

$y = 4 + 9 (2) + 20$

Step 5.3.1.2

Multiply $9$ by $2$ .

$y = 4 + 18 + 20$

Step 5.3.2

Simplify by adding numbers.

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Step 5.3.2.1

Add $4$ and $18$ .

$y = 22 + 20$

Step 5.3.2.2

Add $22$ and $20$ .

$y = 42$

Step 5.4

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

$(2, 42)$

Step 6

These are three possible solutions to the equation.

$(0, 20), (1, 30), (2, 42)$

Step 7