Find the x and y Intercepts f(x)=(5x^2+20x)/(3x+12)

$f (x) = \frac{5 x^{2} + 20 x}{3 x + 12}$

Step 1

Find the x-intercepts.

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

$0 = \frac{5 x^{2} + 20 x}{3 x + 12}$

Solve the equation.

Set the numerator equal to zero.

$5 x^{2} + 20 x = 0$

Solve the equation for $x$ .

Factor $5 x$ out of $5 x^{2} + 20 x$ .

Factor $5 x$ out of $5 x^{2}$ .

$5 x (x) + 20 x = 0$

Factor $5 x$ out of $20 x$ .

$5 x (x) + 5 x (4) = 0$

Factor $5 x$ out of $5 x (x) + 5 x (4)$ .

$5 x (x + 4) = 0$

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

$x = 0$

$x + 4 = 0$

Set $x$ equal to $0$ .

$x = 0$

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

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

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

The final solution is all the values that make $5 x (x + 4) = 0$ true.

$x = 0, - 4$

Exclude the solutions that do not make $0 = \frac{5 x^{2} + 20 x}{3 x + 12}$ true.

$x = 0$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{5 {(0)}^{2} + 20 (0)}{3 (0) + 12}$

Solve the equation.

Remove parentheses.

$y = \frac{5 \cdot 0^{2} + 20 (0)}{3 (0) + 12}$

Remove parentheses.

$y = \frac{5 {(0)}^{2} + 20 (0)}{3 (0) + 12}$

Simplify $\frac{5 {(0)}^{2} + 20 (0)}{3 (0) + 12}$ .

Simplify the numerator.

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

$y = \frac{5 \cdot 0 + 20 (0)}{3 (0) + 12}$

Multiply $5$ by $0$ .

$y = \frac{0 + 20 (0)}{3 (0) + 12}$

Multiply $20$ by $0$ .

$y = \frac{0 + 0}{3 (0) + 12}$

Add $0$ and $0$ .

$y = \frac{0}{3 (0) + 12}$

Simplify the denominator.

Multiply $3$ by $0$ .

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

Add $0$ and $12$ .

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

Divide $0$ by $12$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts f(x)=(5x^2+20x)/(3x+12)

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