Find the x and y Intercepts f(x)=(3x^2-5x)/(x^2-64)

$f (x) = \frac{3 x^{2} - 5 x}{x^{2} - 64}$

Find the x-intercepts.

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

$0 = \frac{3 x^{2} - 5 x}{x^{2} - 64}$

Solve the equation.

Set the numerator equal to zero.

$3 x^{2} - 5 x = 0$

Solve the equation for $x$ .

Factor $x$ out of $3 x^{2} - 5 x$ .

Factor $x$ out of $3 x^{2}$ .

$x (3 x) - 5 x = 0$

Factor $x$ out of $- 5 x$ .

$x (3 x) + x \cdot - 5 = 0$

Factor $x$ out of $x (3 x) + x \cdot - 5$ .

$x (3 x - 5) = 0$

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

$x = 0$

$3 x - 5 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $3 x - 5$ equal to $0$ and solve for $x$ .

Set $3 x - 5$ equal to $0$ .

$3 x - 5 = 0$

Solve $3 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$3 x = 5$

Divide each term in $3 x = 5$ by $3$ and simplify.

Divide each term in $3 x = 5$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3}$

Divide $x$ by $1$ .

$x = \frac{5}{3}$

The final solution is all the values that make $x (3 x - 5) = 0$ true.

$x = 0, \frac{5}{3}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (\frac{5}{3}, 0)$

Find the y-intercepts.

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

$y = \frac{3 {(0)}^{2} - 5 \cdot 0}{{(0)}^{2} - 64}$

Solve the equation.

Remove parentheses.

$y = \frac{3 \cdot 0^{2} - 5 \cdot 0}{{(0)}^{2} - 64}$

Remove parentheses.

$y = \frac{3 \cdot 0^{2} - 5 \cdot 0}{0^{2} - 64}$

Remove parentheses.

$y = \frac{3 {(0)}^{2} - 5 \cdot 0}{{(0)}^{2} - 64}$

Simplify $\frac{3 {(0)}^{2} - 5 \cdot 0}{{(0)}^{2} - 64}$ .

Simplify the numerator.

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

$y = \frac{3 \cdot 0 - 5 \cdot 0}{0^{2} - 64}$

Multiply $3$ by $0$ .

$y = \frac{0 - 5 \cdot 0}{0^{2} - 64}$

Multiply $- 5$ by $0$ .

$y = \frac{0 + 0}{0^{2} - 64}$

Add $0$ and $0$ .

$y = \frac{0}{0^{2} - 64}$

Simplify the denominator.

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

$y = \frac{0}{0 - 64}$

Subtract $64$ from $0$ .

$y = \frac{0}{- 64}$

Divide $0$ by $- 64$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(0, 0), (\frac{5}{3}, 0)$

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

Find the x and y Intercepts f(x)=(3x^2-5x)/(x^2-64)

Related Questions

Support LCMGCF.com by disabling your adblocker.