Find the x and y Intercepts f(x)=(4x^2-1)/(x^2+7x)

$f (x) = \frac{4 x^{2} - 1}{x^{2} + 7 x}$

Find the x-intercepts.

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

$0 = \frac{4 x^{2} - 1}{x^{2} + 7 x}$

Solve the equation.

Set the numerator equal to zero.

$4 x^{2} - 1 = 0$

Solve the equation for $x$ .

Add $1$ to both sides of the equation.

$4 x^{2} = 1$

Divide each term in $4 x^{2} = 1$ by $4$ and simplify.

Divide each term in $4 x^{2} = 1$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{1}{4}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{1}{4}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{\frac{1}{4}}$

Simplify $\pm \sqrt{\frac{1}{4}}$ .

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$x = \pm \frac{\sqrt{1}}{\sqrt{4}}$

Any root of $1$ is $1$ .

$x = \pm \frac{1}{\sqrt{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$x = \pm \frac{1}{\sqrt{2^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{1}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \frac{1}{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \frac{1}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{1}{2}, - \frac{1}{2}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{2}, 0), (- \frac{1}{2}, 0)$

Find the y-intercepts.

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

$y = \frac{4 {(0)}^{2} - 1}{{(0)}^{2} + 7 (0)}$

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): $(\frac{1}{2}, 0), (- \frac{1}{2}, 0)$

y-intercept(s): $None$

Find the x and y Intercepts f(x)=(4x^2-1)/(x^2+7x)

Related Questions

Support LCMGCF.com by disabling your adblocker.