Find the x and y Intercepts f(x)=(x^2-100)/(3x^2-32x+20)

$f (x) = \frac{x^{2} - 100}{3 x^{2} - 32 x + 20}$

Find the x-intercepts.

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

$0 = \frac{x^{2} - 100}{3 x^{2} - 32 x + 20}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} - 100 = 0$

Solve the equation for $x$ .

Add $100$ to both sides of the equation.

$x^{2} = 100$

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

$x = \pm \sqrt{100}$

Simplify $\pm \sqrt{100}$ .

Rewrite $100$ as $10^{2}$ .

$x = \pm \sqrt{10^{2}}$

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

$x = \pm 10$

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.

$x = 10$

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

$x = - 10$

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

$x = 10, - 10$

Exclude the solutions that do not make $0 = \frac{x^{2} - 100}{3 x^{2} - 32 x + 20}$ true.

$x = - 10$

x-intercept(s) in point form.

x-intercept(s): $(- 10, 0)$

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} - 100}{3 {(0)}^{2} - 32 \cdot 0 + 20}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} - 100}{3 {(0)}^{2} - 32 \cdot 0 + 20}$

Remove parentheses.

$y = \frac{0^{2} - 100}{3 \cdot 0^{2} - 32 \cdot 0 + 20}$

Remove parentheses.

$y = \frac{{(0)}^{2} - 100}{3 {(0)}^{2} - 32 \cdot 0 + 20}$

Simplify $\frac{{(0)}^{2} - 100}{3 {(0)}^{2} - 32 \cdot 0 + 20}$ .

Simplify the numerator.

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

$y = \frac{0 - 100}{3 \cdot 0^{2} - 32 \cdot 0 + 20}$

Subtract $100$ from $0$ .

$y = \frac{- 100}{3 \cdot 0^{2} - 32 \cdot 0 + 20}$

Simplify the denominator.

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

$y = \frac{- 100}{3 \cdot 0 - 32 \cdot 0 + 20}$

Multiply $3$ by $0$ .

$y = \frac{- 100}{0 - 32 \cdot 0 + 20}$

Multiply $- 32$ by $0$ .

$y = \frac{- 100}{0 + 0 + 20}$

Add $0$ and $0$ .

$y = \frac{- 100}{0 + 20}$

Add $0$ and $20$ .

$y = \frac{- 100}{20}$

Divide $- 100$ by $20$ .

$y = - 5$

y-intercept(s) in point form.

y-intercept(s): $(0, - 5)$

List the intersections.

x-intercept(s): $(- 10, 0)$

y-intercept(s): $(0, - 5)$

Find the x and y Intercepts f(x)=(x^2-100)/(3x^2-32x+20)

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