Find the x and y Intercepts f(x)=(4x^2-16)/(-5x+10)

$f (x) = \frac{4 x^{2} - 16}{- 5 x + 10}$

Find the x-intercepts.

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

$0 = \frac{4 x^{2} - 16}{- 5 x + 10}$

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 $0 = \frac{4 x^{2} - 16}{- 5 x + 10}$ 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 $y$ .

$y = \frac{4 {(0)}^{2} - 16}{- 5 \cdot 0 + 10}$

Solve the equation.

Remove parentheses.

$y = \frac{4 \cdot 0^{2} - 16}{- 5 \cdot 0 + 10}$

Remove parentheses.

$y = \frac{4 {(0)}^{2} - 16}{- 5 \cdot 0 + 10}$

Simplify $\frac{4 {(0)}^{2} - 16}{- 5 \cdot 0 + 10}$ .

Cancel the common factor of $4 {(0)}^{2} - 16$ and $- 5 \cdot 0 + 10$ .

Factor $2$ out of $4 {(0)}^{2}$ .

$y = \frac{2 (2 {(0)}^{2}) - 16}{- 5 \cdot 0 + 10}$

Factor $2$ out of $- 16$ .

$y = \frac{2 (2 {(0)}^{2}) + 2 (- 8)}{- 5 \cdot 0 + 10}$

Factor $2$ out of $2 (2 {(0)}^{2}) + 2 (- 8)$ .

$y = \frac{2 (2 {(0)}^{2} - 8)}{- 5 \cdot 0 + 10}$

Cancel the common factors.

Factor $2$ out of $- 5 \cdot 0$ .

$y = \frac{2 (2 {(0)}^{2} - 8)}{2 (- 5 \cdot 0) + 10}$

Factor $2$ out of $10$ .

$y = \frac{2 (2 {(0)}^{2} - 8)}{2 (- 5 \cdot 0) + 2 (5)}$

Factor $2$ out of $2 (- 5 \cdot 0) + 2 (5)$ .

$y = \frac{2 (2 {(0)}^{2} - 8)}{2 (- 5 \cdot 0 + 5)}$

Cancel the common factor.

$y = \frac{2 (2 {(0)}^{2} - 8)}{2 (- 5 \cdot 0 + 5)}$

Rewrite the expression.

$y = \frac{2 {(0)}^{2} - 8}{- 5 \cdot 0 + 5}$

Simplify the numerator.

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

$y = \frac{2 \cdot 0 - 8}{- 5 \cdot 0 + 5}$

Multiply $2$ by $0$ .

$y = \frac{0 - 8}{- 5 \cdot 0 + 5}$

Subtract $8$ from $0$ .

$y = \frac{- 8}{- 5 \cdot 0 + 5}$

Simplify the denominator.

Multiply $- 5$ by $0$ .

$y = \frac{- 8}{0 + 5}$

Add $0$ and $5$ .

$y = \frac{- 8}{5}$

Move the negative in front of the fraction.

$y = - \frac{8}{5}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{8}{5})$

List the intersections.

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

y-intercept(s): $(0, - \frac{8}{5})$

Find the x and y Intercepts f(x)=(4x^2-16)/(-5x+10)

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