Find the x and y Intercepts y=-1/7(x-3)(x-8)

$y = - \frac{1}{7} (x - 3) (x - 8)$

Step 1

Find the x-intercepts.

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

$0 = - \frac{1}{7} \cdot ((x - 3) (x - 8))$

Solve the equation.

Rewrite the equation as $- \frac{1}{7} \cdot ((x - 3) (x - 8)) = 0$ .

$- \frac{1}{7} \cdot ((x - 3) (x - 8)) = 0$

Multiply both sides of the equation by $- 7$ .

$- 7 (- \frac{1}{7} \cdot ((x - 3) (x - 8))) = - 7 \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 7 (- \frac{1}{7} \cdot ((x - 3) (x - 8)))$ .

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

Apply the distributive property.

$- 7 (- \frac{1}{7} \cdot (x (x - 8) - 3 (x - 8))) = - 7 \cdot 0$

Apply the distributive property.

$- 7 (- \frac{1}{7} \cdot (x \cdot x + x \cdot - 8 - 3 (x - 8))) = - 7 \cdot 0$

Apply the distributive property.

$- 7 (- \frac{1}{7} \cdot (x \cdot x + x \cdot - 8 - 3 x - 3 \cdot - 8)) = - 7 \cdot 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$- 7 (- \frac{1}{7} \cdot (x^{2} + x \cdot - 8 - 3 x - 3 \cdot - 8)) = - 7 \cdot 0$

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

$- 7 (- \frac{1}{7} \cdot (x^{2} - 8 \cdot x - 3 x - 3 \cdot - 8)) = - 7 \cdot 0$

Multiply $- 3$ by $- 8$ .

$- 7 (- \frac{1}{7} \cdot (x^{2} - 8 x - 3 x + 24)) = - 7 \cdot 0$

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

$- 7 (- \frac{1}{7} \cdot (x^{2} - 11 x + 24)) = - 7 \cdot 0$

Apply the distributive property.

$- 7 (- \frac{1}{7} x^{2} - \frac{1}{7} (- 11 x) - \frac{1}{7} \cdot 24) = - 7 \cdot 0$

Simplify.

Combine $x^{2}$ and $\frac{1}{7}$ .

$- 7 (- \frac{x^{2}}{7} - \frac{1}{7} (- 11 x) - \frac{1}{7} \cdot 24) = - 7 \cdot 0$

Multiply $- \frac{1}{7} (- 11 x)$ .

Multiply $- 11$ by $- 1$ .

$- 7 (- \frac{x^{2}}{7} + 11 (\frac{1}{7}) x - \frac{1}{7} \cdot 24) = - 7 \cdot 0$

Combine $11$ and $\frac{1}{7}$ .

$- 7 (- \frac{x^{2}}{7} + \frac{11}{7} x - \frac{1}{7} \cdot 24) = - 7 \cdot 0$

Combine $\frac{11}{7}$ and $x$ .

$- 7 (- \frac{x^{2}}{7} + \frac{11 x}{7} - \frac{1}{7} \cdot 24) = - 7 \cdot 0$

Multiply $- \frac{1}{7} \cdot 24$ .

Multiply $24$ by $- 1$ .

$- 7 (- \frac{x^{2}}{7} + \frac{11 x}{7} - 24 (\frac{1}{7})) = - 7 \cdot 0$

Combine $- 24$ and $\frac{1}{7}$ .

$- 7 (- \frac{x^{2}}{7} + \frac{11 x}{7} + \frac{- 24}{7}) = - 7 \cdot 0$

Move the negative in front of the fraction.

$- 7 (- \frac{x^{2}}{7} + \frac{11 x}{7} - \frac{24}{7}) = - 7 \cdot 0$

Apply the distributive property.

$- 7 (- \frac{x^{2}}{7}) - 7 \frac{11 x}{7} - 7 (- \frac{24}{7}) = - 7 \cdot 0$

Simplify.

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{x^{2}}{7}$ into the numerator.

$- 7 \frac{- x^{2}}{7} - 7 \frac{11 x}{7} - 7 (- \frac{24}{7}) = - 7 \cdot 0$

Factor $7$ out of $- 7$ .

$7 (- 1) \frac{- x^{2}}{7} - 7 \frac{11 x}{7} - 7 (- \frac{24}{7}) = - 7 \cdot 0$

Cancel the common factor.

$7 \cdot - 1 \frac{- x^{2}}{7} - 7 \frac{11 x}{7} - 7 (- \frac{24}{7}) = - 7 \cdot 0$

Rewrite the expression.

$- - x^{2} - 7 \frac{11 x}{7} - 7 (- \frac{24}{7}) = - 7 \cdot 0$

Multiply $- 1$ by $- 1$ .

$1 x^{2} - 7 \frac{11 x}{7} - 7 (- \frac{24}{7}) = - 7 \cdot 0$

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

$x^{2} - 7 \frac{11 x}{7} - 7 (- \frac{24}{7}) = - 7 \cdot 0$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7$ .

$x^{2} + 7 (- 1) \frac{11 x}{7} - 7 (- \frac{24}{7}) = - 7 \cdot 0$

Cancel the common factor.

$x^{2} + 7 \cdot - 1 \frac{11 x}{7} - 7 (- \frac{24}{7}) = - 7 \cdot 0$

Rewrite the expression.

$x^{2} - (11 x) - 7 (- \frac{24}{7}) = - 7 \cdot 0$

Multiply $11$ by $- 1$ .

$x^{2} - 11 x - 7 (- \frac{24}{7}) = - 7 \cdot 0$

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{24}{7}$ into the numerator.

$x^{2} - 11 x - 7 (\frac{- 24}{7}) = - 7 \cdot 0$

Factor $7$ out of $- 7$ .

$x^{2} - 11 x + 7 (- 1) \frac{- 24}{7} = - 7 \cdot 0$

Cancel the common factor.

$x^{2} - 11 x + 7 \cdot - 1 \frac{- 24}{7} = - 7 \cdot 0$

Rewrite the expression.

$x^{2} - 11 x - - 24 = - 7 \cdot 0$

Multiply $- 1$ by $- 24$ .

$x^{2} - 11 x + 24 = - 7 \cdot 0$

Simplify the right side.

Multiply $- 7$ 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 $y$ .

$y = - \frac{1}{7} \cdot (((0) - 3) ((0) - 8))$

Solve the equation.

Remove parentheses.

$y = - \frac{1}{7} \cdot ((0 - 3) ((0) - 8))$

Remove parentheses.

$y = - \frac{1}{7} \cdot ((0 - 3) (0 - 8))$

Remove parentheses.

$y = - \frac{1}{7} \cdot ((0 - 3) (0 - 8))$

Remove parentheses.

$y = - \frac{1}{7} \cdot (((0) - 3) ((0) - 8))$

Simplify $- \frac{1}{7} \cdot (((0) - 3) ((0) - 8))$ .

Subtract $3$ from $0$ .

$y = - \frac{1}{7} \cdot (- 3 ((0) - 8))$

Subtract $8$ from $0$ .

$y = - \frac{1}{7} \cdot (- 3 \cdot - 8)$

Multiply $- 3$ by $- 8$ .

$y = - \frac{1}{7} \cdot 24$

Multiply $- \frac{1}{7} \cdot 24$ .

Multiply $24$ by $- 1$ .

$y = - 24 (\frac{1}{7})$

Combine $- 24$ and $\frac{1}{7}$ .

$y = \frac{- 24}{7}$

Move the negative in front of the fraction.

$y = - \frac{24}{7}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{24}{7})$

Step 3

List the intersections.

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

y-intercept(s): $(0, - \frac{24}{7})$

Step 4

Find the x and y Intercepts y=-1/7(x-3)(x-8)

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