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

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

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

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

Find the x-intercepts.

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

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

Solve the equation.

Set the numerator equal to zero.

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

Solve the equation for $x$ .

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

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

$x \cdot x + 2 x = 0$

Factor $x$ out of $2 x$ .

$x \cdot x + x \cdot 2 = 0$

Factor $x$ out of $x \cdot x + x \cdot 2$ .

$x (x + 2) = 0$

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

$x = 0$

$x + 2 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

$x = 0, - 2$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- 2, 0)$

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Simplify $\frac{{(0)}^{2} + 2 (0)}{- 4 \cdot 0 + 8}$ .

Simplify the numerator.

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

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

Multiply $2$ by $0$ .

$y = \frac{0 + 0}{- 4 \cdot 0 + 8}$

Add $0$ and $0$ .

$y = \frac{0}{- 4 \cdot 0 + 8}$

Simplify the denominator.

Multiply $- 4$ by $0$ .

$y = \frac{0}{0 + 8}$

Add $0$ and $8$ .

$y = \frac{0}{8}$

Divide $0$ by $8$ .

$y = 0$

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

List the intersections.

x-intercept(s): $(0, 0), (- 2, 0)$

y-intercept(s): $(0, 0)$

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

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