Find the x and y Intercepts y=(3x^2-12)/(8x^2-18x+4)

$y = \frac{3 x^{2} - 12}{8 x^{2} - 18 x + 4}$

Step 1

Find the x-intercepts.

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

$0 = \frac{3 x^{2} - 12}{8 x^{2} - 18 x + 4}$

Solve the equation.

Set the numerator equal to zero.

$3 x^{2} - 12 = 0$

Solve the equation for $x$ .

Add $12$ to both sides of the equation.

$3 x^{2} = 12$

Divide each term in $3 x^{2} = 12$ by $3$ and simplify.

Divide each term in $3 x^{2} = 12$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{12}{3}$

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

$x^{2} = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$x^{2} = 4$

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 $0 = \frac{3 x^{2} - 12}{8 x^{2} - 18 x + 4}$ true.

$x = - 2$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{3 {(0)}^{2} - 12}{8 {(0)}^{2} - 18 \cdot 0 + 4}$

Solve the equation.

Remove parentheses.

$y = \frac{3 \cdot 0^{2} - 12}{8 {(0)}^{2} - 18 \cdot 0 + 4}$

Remove parentheses.

$y = \frac{3 \cdot 0^{2} - 12}{8 \cdot 0^{2} - 18 \cdot 0 + 4}$

Remove parentheses.

$y = \frac{3 {(0)}^{2} - 12}{8 {(0)}^{2} - 18 \cdot 0 + 4}$

Simplify $\frac{3 {(0)}^{2} - 12}{8 {(0)}^{2} - 18 \cdot 0 + 4}$ .

Simplify the numerator.

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

$y = \frac{3 \cdot 0 - 12}{8 \cdot 0^{2} - 18 \cdot 0 + 4}$

Multiply $3$ by $0$ .

$y = \frac{0 - 12}{8 \cdot 0^{2} - 18 \cdot 0 + 4}$

Subtract $12$ from $0$ .

$y = \frac{- 12}{8 \cdot 0^{2} - 18 \cdot 0 + 4}$

Simplify the denominator.

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

$y = \frac{- 12}{8 \cdot 0 - 18 \cdot 0 + 4}$

Multiply $8$ by $0$ .

$y = \frac{- 12}{0 - 18 \cdot 0 + 4}$

Multiply $- 18$ by $0$ .

$y = \frac{- 12}{0 + 0 + 4}$

Add $0$ and $0$ .

$y = \frac{- 12}{0 + 4}$

Add $0$ and $4$ .

$y = \frac{- 12}{4}$

Divide $- 12$ by $4$ .

$y = - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 3)$

Step 4

Find the x and y Intercepts y=(3x^2-12)/(8x^2-18x+4)

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