Find Three Ordered Pair Solutions y=-1/18(x-3)(x-8)

$y = - \frac{1}{18} (x - 3) (x - 8)$

Step 1

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{1}{18} \cdot ((x - 3) (x - 8))$

Remove parentheses.

$y = - \frac{1}{18} \cdot ((x - 3) (x - 8))$

Simplify $- \frac{1}{18} \cdot ((x - 3) (x - 8))$ .

Expand $(x - 3) (x - 8)$ using the FOIL Method.

Apply the distributive property.

$y = - \frac{1}{18} \cdot (x (x - 8) - 3 (x - 8))$

Apply the distributive property.

$y = - \frac{1}{18} \cdot (x \cdot x + x \cdot - 8 - 3 (x - 8))$

Apply the distributive property.

$y = - \frac{1}{18} \cdot (x \cdot x + x \cdot - 8 - 3 x - 3 \cdot - 8)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = - \frac{1}{18} \cdot (x^{2} + x \cdot - 8 - 3 x - 3 \cdot - 8)$

Move $- 8$ to the left of $x$ .

$y = - \frac{1}{18} \cdot (x^{2} - 8 \cdot x - 3 x - 3 \cdot - 8)$

Multiply $- 3$ by $- 8$ .

$y = - \frac{1}{18} \cdot (x^{2} - 8 x - 3 x + 24)$

Subtract $3 x$ from $- 8 x$ .

$y = - \frac{1}{18} \cdot (x^{2} - 11 x + 24)$

Apply the distributive property.

$y = - \frac{1}{18} x^{2} - \frac{1}{18} (- 11 x) - \frac{1}{18} \cdot 24$

Simplify.

Combine $x^{2}$ and $\frac{1}{18}$ .

$y = - \frac{x^{2}}{18} - \frac{1}{18} (- 11 x) - \frac{1}{18} \cdot 24$

Multiply $- \frac{1}{18} (- 11 x)$ .

Multiply $- 11$ by $- 1$ .

$y = - \frac{x^{2}}{18} + 11 (\frac{1}{18}) x - \frac{1}{18} \cdot 24$

Combine $11$ and $\frac{1}{18}$ .

$y = - \frac{x^{2}}{18} + \frac{11}{18} x - \frac{1}{18} \cdot 24$

Combine $\frac{11}{18}$ and $x$ .

$y = - \frac{x^{2}}{18} + \frac{11 x}{18} - \frac{1}{18} \cdot 24$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{18}$ into the numerator.

$y = - \frac{x^{2}}{18} + \frac{11 x}{18} + \frac{- 1}{18} \cdot 24$

Factor $6$ out of $18$ .

$y = - \frac{x^{2}}{18} + \frac{11 x}{18} + \frac{- 1}{6 (3)} \cdot 24$

Factor $6$ out of $24$ .

$y = - \frac{x^{2}}{18} + \frac{11 x}{18} + \frac{- 1}{6 \cdot 3} \cdot (6 \cdot 4)$

Cancel the common factor.

$y = - \frac{x^{2}}{18} + \frac{11 x}{18} + \frac{- 1}{6 \cdot 3} \cdot (6 \cdot 4)$

Rewrite the expression.

$y = - \frac{x^{2}}{18} + \frac{11 x}{18} + \frac{- 1}{3} \cdot 4$

Combine $\frac{- 1}{3}$ and $4$ .

$y = - \frac{x^{2}}{18} + \frac{11 x}{18} + \frac{- 1 \cdot 4}{3}$

Multiply $- 1$ by $4$ .

$y = - \frac{x^{2}}{18} + \frac{11 x}{18} + \frac{- 4}{3}$

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{18} + \frac{11 x}{18} - \frac{4}{3}$

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.

$y = - \frac{0^{2}}{18} + \frac{11 (0)}{18} - \frac{4}{3}$

Remove parentheses.

$y = - \frac{{(0)}^{2}}{18} + \frac{11 (0)}{18} - \frac{4}{3}$

Simplify $- \frac{{(0)}^{2}}{18} + \frac{11 (0)}{18} - \frac{4}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{- {(0)}^{2} + 11 (0)}{18} + \frac{- 4}{3}$

Simplify each term.

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

$y = \frac{- 0 + 11 (0)}{18} + \frac{- 4}{3}$

Multiply $- 1$ by $0$ .

$y = \frac{0 + 11 (0)}{18} + \frac{- 4}{3}$

Multiply $11$ by $0$ .

$y = \frac{0 + 0}{18} + \frac{- 4}{3}$

Add $0$ and $0$ .

$y = \frac{0}{18} + \frac{- 4}{3}$

Simplify each term.

Divide $0$ by $18$ .

$y = 0 + \frac{- 4}{3}$

Move the negative in front of the fraction.

$y = 0 - \frac{4}{3}$

Subtract $\frac{4}{3}$ from $0$ .

$y = - \frac{4}{3}$

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

$(0, - \frac{4}{3})$

Step 4

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

Remove parentheses.

$y = - \frac{1^{2}}{18} + \frac{11 (1)}{18} - \frac{4}{3}$

Remove parentheses.

$y = - \frac{{(1)}^{2}}{18} + \frac{11 (1)}{18} - \frac{4}{3}$

Simplify $- \frac{{(1)}^{2}}{18} + \frac{11 (1)}{18} - \frac{4}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{- {(1)}^{2} + 11 (1)}{18} + \frac{- 4}{3}$

Simplify each term.

One to any power is one.

$y = \frac{- 1 \cdot 1 + 11 (1)}{18} + \frac{- 4}{3}$

Multiply $- 1$ by $1$ .

$y = \frac{- 1 + 11 (1)}{18} + \frac{- 4}{3}$

Multiply $11$ by $1$ .

$y = \frac{- 1 + 11}{18} + \frac{- 4}{3}$

Add $- 1$ and $11$ .

$y = \frac{10}{18} + \frac{- 4}{3}$

Simplify each term.

Cancel the common factor of $10$ and $18$ .

Factor $2$ out of $10$ .

$y = \frac{2 (5)}{18} + \frac{- 4}{3}$

Cancel the common factors.

Factor $2$ out of $18$ .

$y = \frac{2 \cdot 5}{2 \cdot 9} + \frac{- 4}{3}$

Cancel the common factor.

$y = \frac{2 \cdot 5}{2 \cdot 9} + \frac{- 4}{3}$

Rewrite the expression.

$y = \frac{5}{9} + \frac{- 4}{3}$

Move the negative in front of the fraction.

$y = \frac{5}{9} - \frac{4}{3}$

To write $- \frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{5}{9} - \frac{4}{3} \cdot \frac{3}{3}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{3}$ by $\frac{3}{3}$ .

$y = \frac{5}{9} - \frac{4 \cdot 3}{3 \cdot 3}$

Multiply $3$ by $3$ .

$y = \frac{5}{9} - \frac{4 \cdot 3}{9}$

Combine the numerators over the common denominator.

$y = \frac{5 - 4 \cdot 3}{9}$

Simplify the numerator.

Multiply $- 4$ by $3$ .

$y = \frac{5 - 12}{9}$

Subtract $12$ from $5$ .

$y = \frac{- 7}{9}$

Move the negative in front of the fraction.

$y = - \frac{7}{9}$

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

$(1, - \frac{7}{9})$

Step 5

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

Remove parentheses.

$y = - \frac{2^{2}}{18} + \frac{11 (2)}{18} - \frac{4}{3}$

Remove parentheses.

$y = - \frac{{(2)}^{2}}{18} + \frac{11 (2)}{18} - \frac{4}{3}$

Simplify $- \frac{{(2)}^{2}}{18} + \frac{11 (2)}{18} - \frac{4}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{- {(2)}^{2} + 11 (2)}{18} + \frac{- 4}{3}$

Simplify each term.

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

$y = \frac{- 1 \cdot 4 + 11 (2)}{18} + \frac{- 4}{3}$

Multiply $- 1$ by $4$ .

$y = \frac{- 4 + 11 (2)}{18} + \frac{- 4}{3}$

Multiply $11$ by $2$ .

$y = \frac{- 4 + 22}{18} + \frac{- 4}{3}$

Add $- 4$ and $22$ .

$y = \frac{18}{18} + \frac{- 4}{3}$

Simplify each term.

Divide $18$ by $18$ .

$y = 1 + \frac{- 4}{3}$

Move the negative in front of the fraction.

$y = 1 - \frac{4}{3}$

Simplify the expression.

Write $1$ as a fraction with a common denominator.

$y = \frac{3}{3} - \frac{4}{3}$

Combine the numerators over the common denominator.

$y = \frac{3 - 4}{3}$

Subtract $4$ from $3$ .

$y = \frac{- 1}{3}$

Move the negative in front of the fraction.

$y = - \frac{1}{3}$

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

$(2, - \frac{1}{3})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{4}{3}), (1, - \frac{7}{9}), (2, - \frac{1}{3})$

Step 7

Find Three Ordered Pair Solutions y=-1/18(x-3)(x-8)

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