Find the x and y Intercepts (-3x^2+21x-36)/(5x-20)

$\frac{- 3 x^{2} + 21 x - 36}{5 x - 20}$

Write $\frac{- 3 x^{2} + 21 x - 36}{5 x - 20}$ as an equation.

$y = \frac{- 3 x^{2} + 21 x - 36}{5 x - 20}$

Find the x-intercepts.

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

$0 = \frac{- 3 x^{2} + 21 x - 36}{5 x - 20}$

Solve the equation.

Set the numerator equal to zero.

$- 3 x^{2} + 21 x - 36 = 0$

Solve the equation for $x$ .

Factor the left side of the equation.

Factor $- 3$ out of $- 3 x^{2} + 21 x - 36$ .

Factor $- 3$ out of $- 3 x^{2}$ .

$- 3 x^{2} + 21 x - 36 = 0$

Factor $- 3$ out of $21 x$ .

$- 3 x^{2} - 3 (- 7 x) - 36 = 0$

Factor $- 3$ out of $- 36$ .

$- 3 x^{2} - 3 (- 7 x) - 3 \cdot 12 = 0$

Factor $- 3$ out of $- 3 (x^{2}) - 3 (- 7 x)$ .

$- 3 (x^{2} - 7 x) - 3 \cdot 12 = 0$

Factor $- 3$ out of $- 3 (x^{2} - 7 x) - 3 (12)$ .

$- 3 (x^{2} - 7 x + 12) = 0$

Factor.

Factor $x^{2} - 7 x + 12$ 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 $12$ and whose sum is $- 7$ .

$- 4, - 3$

Write the factored form using these integers.

$- 3 ((x - 4) (x - 3)) = 0$

Remove unnecessary parentheses.

$- 3 (x - 4) (x - 3) = 0$

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

$x - 4 = 0$

$x - 3 = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

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 $- 3 (x - 4) (x - 3) = 0$ true.

$x = 4, 3$

Exclude the solutions that do not make $0 = \frac{- 3 x^{2} + 21 x - 36}{5 x - 20}$ true.

$x = 3$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = \frac{- 3 {(0)}^{2} + 21 (0) - 36}{5 (0) - 20}$

Solve the equation.

Remove parentheses.

$y = \frac{- 3 \cdot 0^{2} + 21 (0) - 36}{5 (0) - 20}$

Remove parentheses.

$y = \frac{- 3 {(0)}^{2} + 21 (0) - 36}{5 (0) - 20}$

Simplify $\frac{- 3 {(0)}^{2} + 21 (0) - 36}{5 (0) - 20}$ .

Simplify the numerator.

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

$y = \frac{- 3 \cdot 0 + 21 (0) - 36}{5 (0) - 20}$

Multiply $- 3$ by $0$ .

$y = \frac{0 + 21 (0) - 36}{5 (0) - 20}$

Multiply $21$ by $0$ .

$y = \frac{0 + 0 - 36}{5 (0) - 20}$

Add $0$ and $0$ .

$y = \frac{0 - 36}{5 (0) - 20}$

Subtract $36$ from $0$ .

$y = \frac{- 36}{5 (0) - 20}$

Simplify the denominator.

Multiply $5$ by $0$ .

$y = \frac{- 36}{0 - 20}$

Subtract $20$ from $0$ .

$y = \frac{- 36}{- 20}$

Cancel the common factor of $- 36$ and $- 20$ .

Factor $- 4$ out of $- 36$ .

$y = \frac{- 4 (9)}{- 20}$

Cancel the common factors.

Factor $- 4$ out of $- 20$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{9}{5})$

List the intersections.

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

y-intercept(s): $(0, \frac{9}{5})$

Find the x and y Intercepts (-3x^2+21x-36)/(5x-20)

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