Find the x and y Intercepts f(x)=(-3x^2+75)/(5x^2+35x+50)

$f (x) = \frac{- 3 x^{2} + 75}{5 x^{2} + 35 x + 50}$

Step 1

Find the x-intercepts.

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

$0 = \frac{- 3 x^{2} + 75}{5 x^{2} + 35 x + 50}$

Solve the equation.

Set the numerator equal to zero.

$- 3 x^{2} + 75 = 0$

Solve the equation for $x$ .

Subtract $75$ from both sides of the equation.

$- 3 x^{2} = - 75$

Divide each term in $- 3 x^{2} = - 75$ by $- 3$ and simplify.

Divide each term in $- 3 x^{2} = - 75$ by $- 3$ .

$\frac{- 3 x^{2}}{- 3} = \frac{- 75}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x^{2}}{- 3} = \frac{- 75}{- 3}$

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

$x^{2} = \frac{- 75}{- 3}$

Simplify the right side.

Divide $- 75$ by $- 3$ .

$x^{2} = 25$

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

$x = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt{5^{2}}$

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

$x = \pm 5$

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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$

Exclude the solutions that do not make $0 = \frac{- 3 x^{2} + 75}{5 x^{2} + 35 x + 50}$ true.

$x = 5$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{- 3 {(0)}^{2} + 75}{5 {(0)}^{2} + 35 (0) + 50}$

Solve the equation.

Remove parentheses.

$y = \frac{- 3 \cdot 0^{2} + 75}{5 {(0)}^{2} + 35 (0) + 50}$

Remove parentheses.

$y = \frac{- 3 \cdot 0^{2} + 75}{5 \cdot 0^{2} + 35 (0) + 50}$

Remove parentheses.

$y = \frac{- 3 {(0)}^{2} + 75}{5 {(0)}^{2} + 35 (0) + 50}$

Simplify $\frac{- 3 {(0)}^{2} + 75}{5 {(0)}^{2} + 35 (0) + 50}$ .

Simplify the numerator.

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

$y = \frac{- 3 \cdot 0 + 75}{5 \cdot 0^{2} + 35 (0) + 50}$

Multiply $- 3$ by $0$ .

$y = \frac{0 + 75}{5 \cdot 0^{2} + 35 (0) + 50}$

Add $0$ and $75$ .

$y = \frac{75}{5 \cdot 0^{2} + 35 (0) + 50}$

Simplify the denominator.

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

$y = \frac{75}{5 \cdot 0 + 35 (0) + 50}$

Multiply $5$ by $0$ .

$y = \frac{75}{0 + 35 (0) + 50}$

Multiply $35$ by $0$ .

$y = \frac{75}{0 + 0 + 50}$

Add $0$ and $0$ .

$y = \frac{75}{0 + 50}$

Add $0$ and $50$ .

$y = \frac{75}{50}$

Cancel the common factor of $75$ and $50$ .

Factor $25$ out of $75$ .

$y = \frac{25 (3)}{50}$

Cancel the common factors.

Factor $25$ out of $50$ .

$y = \frac{25 \cdot 3}{25 \cdot 2}$

Cancel the common factor.

$y = \frac{25 \cdot 3}{25 \cdot 2}$

Rewrite the expression.

$y = \frac{3}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{3}{2})$

Step 3

List the intersections.

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

y-intercept(s): $(0, \frac{3}{2})$

Step 4

Find the x and y Intercepts f(x)=(-3x^2+75)/(5x^2+35x+50)

Related Questions

Support LCMGCF.com by disabling your adblocker.