Find the x and y Intercepts 12/(x^2-3x-23)

$\frac{12}{x^{2} - 3 x - 23}$

Step 1

Write $\frac{12}{x^{2} - 3 x - 23}$ as an equation.

$y = \frac{12}{x^{2} - 3 x - 23}$

Step 2

Find the x-intercepts.

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

$0 = \frac{12}{x^{2} - 3 x - 23}$

Solve the equation.

Set the numerator equal to zero.

$12 = 0$

Since $12 \neq 0$ , there are no solutions.

No solution

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

x-intercept(s): $None$

Step 3

Find the y-intercepts.

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

$y = \frac{12}{{(0)}^{2} - 3 \cdot 0 - 23}$

Solve the equation.

Remove parentheses.

$y = \frac{12}{0^{2} - 3 \cdot 0 - 23}$

Remove parentheses.

$y = \frac{12}{{(0)}^{2} - 3 \cdot 0 - 23}$

Simplify $\frac{12}{{(0)}^{2} - 3 \cdot 0 - 23}$ .

Simplify the denominator.

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

$y = \frac{12}{0 - 3 \cdot 0 - 23}$

Multiply $- 3$ by $0$ .

$y = \frac{12}{0 + 0 - 23}$

Add $0$ and $0$ .

$y = \frac{12}{0 - 23}$

Subtract $23$ from $0$ .

$y = \frac{12}{- 23}$

Move the negative in front of the fraction.

$y = - \frac{12}{23}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{12}{23})$

Step 4

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{12}{23})$

Step 5