Find the x and y Intercepts f(x)=(-4x+12)/(2x^2-x-15)

$f (x) = \frac{- 4 x + 12}{2 x^{2} - x - 15}$

Step 1

Find the x-intercepts.

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

$0 = \frac{- 4 x + 12}{2 x^{2} - x - 15}$

Solve the equation.

Set the numerator equal to zero.

$- 4 x + 12 = 0$

Solve the equation for $x$ .

Subtract $12$ from both sides of the equation.

$- 4 x = - 12$

Divide each term in $- 4 x = - 12$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 12$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 12}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 4}$

Simplify the right side.

Divide $- 12$ by $- 4$ .

$x = 3$

Exclude the solutions that do not make $0 = \frac{- 4 x + 12}{2 x^{2} - x - 15}$ true.

$No solution$

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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

$y = \frac{- 4 \cdot 0 + 12}{2 {(0)}^{2} - (0) - 15}$

Solve the equation.

Remove parentheses.

$y = \frac{- 4 \cdot 0 + 12}{2 \cdot 0^{2} - (0) - 15}$

Remove parentheses.

$y = \frac{- 4 \cdot 0 + 12}{2 {(0)}^{2} - (0) - 15}$

Simplify $\frac{- 4 \cdot 0 + 12}{2 {(0)}^{2} - (0) - 15}$ .

Simplify the numerator.

Multiply $- 4$ by $0$ .

$y = \frac{0 + 12}{2 \cdot 0^{2} - (0) - 15}$

Add $0$ and $12$ .

$y = \frac{12}{2 \cdot 0^{2} - (0) - 15}$

Simplify the denominator.

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

$y = \frac{12}{2 \cdot 0 - (0) - 15}$

Multiply $2$ by $0$ .

$y = \frac{12}{0 - (0) - 15}$

Multiply $- 1$ by $0$ .

$y = \frac{12}{0 + 0 - 15}$

Add $0$ and $0$ .

$y = \frac{12}{0 - 15}$

Subtract $15$ from $0$ .

$y = \frac{12}{- 15}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $12$ and $- 15$ .

Factor $3$ out of $12$ .

$y = \frac{3 (4)}{- 15}$

Cancel the common factors.

Factor $3$ out of $- 15$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{4}{5})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{4}{5})$

Step 4

Find the x and y Intercepts f(x)=(-4x+12)/(2x^2-x-15)

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