Find the x and y Intercepts f(x)=(x^2-4)/(2x^2-11x+14)

$f (x) = \frac{x^{2} - 4}{2 x^{2} - 11 x + 14}$

Find the x-intercepts.

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

$0 = \frac{x^{2} - 4}{2 x^{2} - 11 x + 14}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} - 4 = 0$

Solve the equation for $x$ .

Add $4$ to both sides of the equation.

$x^{2} = 4$

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

$x = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

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

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

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

$x = \pm 2$

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$

Exclude the solutions that do not make $0 = \frac{x^{2} - 4}{2 x^{2} - 11 x + 14}$ true.

$x = - 2$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} - 4}{2 {(0)}^{2} - 11 \cdot 0 + 14}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} - 4}{2 {(0)}^{2} - 11 \cdot 0 + 14}$

Remove parentheses.

$y = \frac{0^{2} - 4}{2 \cdot 0^{2} - 11 \cdot 0 + 14}$

Remove parentheses.

$y = \frac{{(0)}^{2} - 4}{2 {(0)}^{2} - 11 \cdot 0 + 14}$

Simplify $\frac{{(0)}^{2} - 4}{2 {(0)}^{2} - 11 \cdot 0 + 14}$ .

Simplify the numerator.

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

$y = \frac{0 - 4}{2 \cdot 0^{2} - 11 \cdot 0 + 14}$

Subtract $4$ from $0$ .

$y = \frac{- 4}{2 \cdot 0^{2} - 11 \cdot 0 + 14}$

Simplify the denominator.

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

$y = \frac{- 4}{2 \cdot 0 - 11 \cdot 0 + 14}$

Multiply $2$ by $0$ .

$y = \frac{- 4}{0 - 11 \cdot 0 + 14}$

Multiply $- 11$ by $0$ .

$y = \frac{- 4}{0 + 0 + 14}$

Add $0$ and $0$ .

$y = \frac{- 4}{0 + 14}$

Add $0$ and $14$ .

$y = \frac{- 4}{14}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 4$ and $14$ .

Factor $2$ out of $- 4$ .

$y = \frac{2 (- 2)}{14}$

Cancel the common factors.

Factor $2$ out of $14$ .

$y = \frac{2 \cdot - 2}{2 \cdot 7}$

Cancel the common factor.

$y = \frac{2 \cdot - 2}{2 \cdot 7}$

Rewrite the expression.

$y = \frac{- 2}{7}$

Move the negative in front of the fraction.

$y = - \frac{2}{7}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{2}{7})$

List the intersections.

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

y-intercept(s): $(0, - \frac{2}{7})$

Find the x and y Intercepts f(x)=(x^2-4)/(2x^2-11x+14)

Related Questions

Support LCMGCF.com by disabling your adblocker.