Find the x and y Intercepts (2x^2+6x)/(-4x^2+8x)

$\frac{2 x^{2} + 6 x}{- 4 x^{2} + 8 x}$

Write $\frac{2 x^{2} + 6 x}{- 4 x^{2} + 8 x}$ as an equation.

$y = \frac{2 x^{2} + 6 x}{- 4 x^{2} + 8 x}$

Find the x-intercepts.

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

$0 = \frac{2 x^{2} + 6 x}{- 4 x^{2} + 8 x}$

Solve the equation.

Set the numerator equal to zero.

$2 x^{2} + 6 x = 0$

Solve the equation for $x$ .

Factor $2 x$ out of $2 x^{2} + 6 x$ .

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

$2 x (x) + 6 x = 0$

Factor $2 x$ out of $6 x$ .

$2 x (x) + 2 x (3) = 0$

Factor $2 x$ out of $2 x (x) + 2 x (3)$ .

$2 x (x + 3) = 0$

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

$x = 0$

$x + 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

The final solution is all the values that make $2 x (x + 3) = 0$ true.

$x = 0, - 3$

Exclude the solutions that do not make $0 = \frac{2 x^{2} + 6 x}{- 4 x^{2} + 8 x}$ 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 $y$ .

$y = \frac{2 {(0)}^{2} + 6 (0)}{- 4 {(0)}^{2} + 8 (0)}$

The equation has an undefined fraction.

Undefined

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

y-intercept(s): $None$

List the intersections.

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

y-intercept(s): $None$