Find the x and y Intercepts y=-1/36(x-3)(x-8)

$y = - \frac{1}{36} (x - 3) (x - 8)$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - \frac{1}{36} \cdot ((x - 3) (x - 8))$

Solve the equation.

Rewrite the equation as $- \frac{1}{36} \cdot ((x - 3) (x - 8)) = 0$ .

$- \frac{1}{36} \cdot ((x - 3) (x - 8)) = 0$

Multiply both sides of the equation by $- 36$ .

$- 36 (- \frac{1}{36} \cdot ((x - 3) (x - 8))) = - 36 \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 36 (- \frac{1}{36} \cdot ((x - 3) (x - 8)))$ .

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

Apply the distributive property.

$- 36 (- \frac{1}{36} \cdot (x (x - 8) - 3 (x - 8))) = - 36 \cdot 0$

Apply the distributive property.

$- 36 (- \frac{1}{36} \cdot (x \cdot x + x \cdot - 8 - 3 (x - 8))) = - 36 \cdot 0$

Apply the distributive property.

$- 36 (- \frac{1}{36} \cdot (x \cdot x + x \cdot - 8 - 3 x - 3 \cdot - 8)) = - 36 \cdot 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$- 36 (- \frac{1}{36} \cdot (x^{2} + x \cdot - 8 - 3 x - 3 \cdot - 8)) = - 36 \cdot 0$

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

$- 36 (- \frac{1}{36} \cdot (x^{2} - 8 \cdot x - 3 x - 3 \cdot - 8)) = - 36 \cdot 0$

Multiply $- 3$ by $- 8$ .

$- 36 (- \frac{1}{36} \cdot (x^{2} - 8 x - 3 x + 24)) = - 36 \cdot 0$

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

$- 36 (- \frac{1}{36} \cdot (x^{2} - 11 x + 24)) = - 36 \cdot 0$

Apply the distributive property.

$- 36 (- \frac{1}{36} x^{2} - \frac{1}{36} (- 11 x) - \frac{1}{36} \cdot 24) = - 36 \cdot 0$

Simplify.

Combine $x^{2}$ and $\frac{1}{36}$ .

$- 36 (- \frac{x^{2}}{36} - \frac{1}{36} (- 11 x) - \frac{1}{36} \cdot 24) = - 36 \cdot 0$

Multiply $- \frac{1}{36} (- 11 x)$ .

Multiply $- 11$ by $- 1$ .

$- 36 (- \frac{x^{2}}{36} + 11 (\frac{1}{36}) x - \frac{1}{36} \cdot 24) = - 36 \cdot 0$

Combine $11$ and $\frac{1}{36}$ .

$- 36 (- \frac{x^{2}}{36} + \frac{11}{36} x - \frac{1}{36} \cdot 24) = - 36 \cdot 0$

Combine $\frac{11}{36}$ and $x$ .

$- 36 (- \frac{x^{2}}{36} + \frac{11 x}{36} - \frac{1}{36} \cdot 24) = - 36 \cdot 0$

Cancel the common factor of $12$ .

Move the leading negative in $- \frac{1}{36}$ into the numerator.

$- 36 (- \frac{x^{2}}{36} + \frac{11 x}{36} + \frac{- 1}{36} \cdot 24) = - 36 \cdot 0$

Factor $12$ out of $36$ .

$- 36 (- \frac{x^{2}}{36} + \frac{11 x}{36} + \frac{- 1}{12 (3)} \cdot 24) = - 36 \cdot 0$

Factor $12$ out of $24$ .

$- 36 (- \frac{x^{2}}{36} + \frac{11 x}{36} + \frac{- 1}{12 \cdot 3} \cdot (12 \cdot 2)) = - 36 \cdot 0$

Cancel the common factor.

$- 36 (- \frac{x^{2}}{36} + \frac{11 x}{36} + \frac{- 1}{12 \cdot 3} \cdot (12 \cdot 2)) = - 36 \cdot 0$

Rewrite the expression.

$- 36 (- \frac{x^{2}}{36} + \frac{11 x}{36} + \frac{- 1}{3} \cdot 2) = - 36 \cdot 0$

Combine $\frac{- 1}{3}$ and $2$ .

$- 36 (- \frac{x^{2}}{36} + \frac{11 x}{36} + \frac{- 1 \cdot 2}{3}) = - 36 \cdot 0$

Multiply $- 1$ by $2$ .

$- 36 (- \frac{x^{2}}{36} + \frac{11 x}{36} + \frac{- 2}{3}) = - 36 \cdot 0$

Move the negative in front of the fraction.

$- 36 (- \frac{x^{2}}{36} + \frac{11 x}{36} - \frac{2}{3}) = - 36 \cdot 0$

Apply the distributive property.

$- 36 (- \frac{x^{2}}{36}) - 36 \frac{11 x}{36} - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Simplify.

Cancel the common factor of $36$ .

Move the leading negative in $- \frac{x^{2}}{36}$ into the numerator.

$- 36 \frac{- x^{2}}{36} - 36 \frac{11 x}{36} - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Factor $36$ out of $- 36$ .

$36 (- 1) \frac{- x^{2}}{36} - 36 \frac{11 x}{36} - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Cancel the common factor.

$36 \cdot - 1 \frac{- x^{2}}{36} - 36 \frac{11 x}{36} - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Rewrite the expression.

$- - x^{2} - 36 \frac{11 x}{36} - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Multiply $- 1$ by $- 1$ .

$1 x^{2} - 36 \frac{11 x}{36} - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Multiply $x^{2}$ by $1$ .

$x^{2} - 36 \frac{11 x}{36} - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Cancel the common factor of $36$ .

Factor $36$ out of $- 36$ .

$x^{2} + 36 (- 1) \frac{11 x}{36} - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Cancel the common factor.

$x^{2} + 36 \cdot - 1 \frac{11 x}{36} - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Rewrite the expression.

$x^{2} - (11 x) - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Multiply $11$ by $- 1$ .

$x^{2} - 11 x - 36 (- \frac{2}{3}) = - 36 \cdot 0$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$x^{2} - 11 x - 36 (\frac{- 2}{3}) = - 36 \cdot 0$

Factor $3$ out of $- 36$ .

$x^{2} - 11 x + 3 (- 12) \frac{- 2}{3} = - 36 \cdot 0$

Cancel the common factor.

$x^{2} - 11 x + 3 \cdot - 12 \frac{- 2}{3} = - 36 \cdot 0$

Rewrite the expression.

$x^{2} - 11 x - 12 \cdot - 2 = - 36 \cdot 0$

Multiply $- 12$ by $- 2$ .

$x^{2} - 11 x + 24 = - 36 \cdot 0$

Simplify the right side.

Multiply $- 36$ by $0$ .

$x^{2} - 11 x + 24 = 0$

Factor $x^{2} - 11 x + 24$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $24$ and whose sum is $- 11$ .

$- 8, - 3$

Write the factored form using these integers.

$(x - 8) (x - 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 8 = 0$

$x - 3 = 0$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

The final solution is all the values that make $(x - 8) (x - 3) = 0$ true.

$x = 8, 3$

x-intercept(s) in point form.

x-intercept(s): $(8, 0), (3, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - \frac{1}{36} \cdot (((0) - 3) ((0) - 8))$

Solve the equation.

Remove parentheses.

$y = - \frac{1}{36} \cdot ((0 - 3) ((0) - 8))$

Remove parentheses.

$y = - \frac{1}{36} \cdot ((0 - 3) (0 - 8))$

Remove parentheses.

$y = - \frac{1}{36} \cdot ((0 - 3) (0 - 8))$

Remove parentheses.

$y = - \frac{1}{36} \cdot (((0) - 3) ((0) - 8))$

Simplify $- \frac{1}{36} \cdot (((0) - 3) ((0) - 8))$ .

Subtract $3$ from $0$ .

$y = - \frac{1}{36} \cdot (- 3 ((0) - 8))$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{36}$ into the numerator.

$y = \frac{- 1}{36} \cdot (- 3 ((0) - 8))$

Factor $3$ out of $36$ .

$y = \frac{- 1}{3 (12)} \cdot (- 3 ((0) - 8))$

Factor $3$ out of $- 3 ((0) - 8)$ .

$y = \frac{- 1}{3 (12)} \cdot (3 (- ((0) - 8)))$

Cancel the common factor.

$y = \frac{- 1}{3 \cdot 12} \cdot (3 (- ((0) - 8)))$

Rewrite the expression.

$y = \frac{- 1}{12} \cdot (- ((0) - 8))$

Simplify the expression.

Move the negative in front of the fraction.

$y = - \frac{1}{12} \cdot (- ((0) - 8))$

Subtract $8$ from $0$ .

$y = - \frac{1}{12} \cdot (- - 8)$

Multiply $- 1$ by $- 8$ .

$y = - \frac{1}{12} \cdot 8$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{12}$ into the numerator.

$y = \frac{- 1}{12} \cdot 8$

Factor $4$ out of $12$ .

$y = \frac{- 1}{4 (3)} \cdot 8$

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{- 1}{3} \cdot 2$

Combine $\frac{- 1}{3}$ and $2$ .

$y = \frac{- 1 \cdot 2}{3}$

Simplify the expression.

Multiply $- 1$ by $2$ .

$y = \frac{- 2}{3}$

Move the negative in front of the fraction.

$y = - \frac{2}{3}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{2}{3})$

Step 3

List the intersections.

x-intercept(s): $(8, 0), (3, 0)$

y-intercept(s): $(0, - \frac{2}{3})$

Step 4

Find the x and y Intercepts y=-1/36(x-3)(x-8)

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