Find the x and y Intercepts (4x^2-16)/(-3x^2+6x)

$\frac{4 x^{2} - 16}{- 3 x^{2} + 6 x}$

Step 1

Write $\frac{4 x^{2} - 16}{- 3 x^{2} + 6 x}$ as an equation.

$y = \frac{4 x^{2} - 16}{- 3 x^{2} + 6 x}$

Step 2

Find the x-intercepts.

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

$0 = \frac{4 x^{2} - 16}{- 3 x^{2} + 6 x}$

Solve the equation.

Set the numerator equal to zero.

$4 x^{2} - 16 = 0$

Solve the equation for $x$ .

Add $16$ to both sides of the equation.

$4 x^{2} = 16$

Divide each term in $4 x^{2} = 16$ by $4$ and simplify.

Divide each term in $4 x^{2} = 16$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{16}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{16}{4}$

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

$x^{2} = \frac{16}{4}$

Simplify the right side.

Divide $16$ by $4$ .

$x^{2} = 4$

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 $0 = \frac{4 x^{2} - 16}{- 3 x^{2} + 6 x}$ true.

$x = - 2$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

$y = \frac{4 {(0)}^{2} - 16}{- 3 {(0)}^{2} + 6 (0)}$

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): $None$

Step 4

List the intersections.

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

y-intercept(s): $None$

Step 5

Find the x and y Intercepts (4x^2-16)/(-3x^2+6x)

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