Find the x and y Intercepts f(x)=(2x^2-6x)/(5x-15)

$f (x) = \frac{2 x^{2} - 6 x}{5 x - 15}$

Step 1

Find the x-intercepts.

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

$0 = \frac{2 x^{2} - 6 x}{5 x - 15}$

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 $0$ .

$x - 3 = 0$

Add $3$ to 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 $0 = \frac{2 x^{2} - 6 x}{5 x - 15}$ 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 $y$ .

$y = \frac{2 {(0)}^{2} - 6 \cdot 0}{5 (0) - 15}$

Solve the equation.

Remove parentheses.

$y = \frac{2 \cdot 0^{2} - 6 \cdot 0}{5 (0) - 15}$

Remove parentheses.

$y = \frac{2 {(0)}^{2} - 6 \cdot 0}{5 (0) - 15}$

Simplify $\frac{2 {(0)}^{2} - 6 \cdot 0}{5 (0) - 15}$ .

Simplify the numerator.

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

$y = \frac{2 \cdot 0 - 6 \cdot 0}{5 (0) - 15}$

Multiply $2$ by $0$ .

$y = \frac{0 - 6 \cdot 0}{5 (0) - 15}$

Multiply $- 6$ by $0$ .

$y = \frac{0 + 0}{5 (0) - 15}$

Add $0$ and $0$ .

$y = \frac{0}{5 (0) - 15}$

Simplify the denominator.

Multiply $5$ by $0$ .

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

Subtract $15$ from $0$ .

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

Divide $0$ by $- 15$ .

$y = 0$

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)=(2x^2-6x)/(5x-15)

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