Find the x and y Intercepts f(x)=(5x^2+7x)/(2x^2-6x-80)

$f (x) = \frac{5 x^{2} + 7 x}{2 x^{2} - 6 x - 80}$

Find the x-intercepts.

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

$0 = \frac{5 x^{2} + 7 x}{2 x^{2} - 6 x - 80}$

Solve the equation.

Set the numerator equal to zero.

$5 x^{2} + 7 x = 0$

Solve the equation for $x$ .

Factor $x$ out of $5 x^{2} + 7 x$ .

Factor $x$ out of $5 x^{2}$ .

$x (5 x) + 7 x = 0$

Factor $x$ out of $7 x$ .

$x (5 x) + x \cdot 7 = 0$

Factor $x$ out of $x (5 x) + x \cdot 7$ .

$x (5 x + 7) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$5 x + 7 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $5 x + 7$ equal to $0$ and solve for $x$ .

Set $5 x + 7$ equal to $0$ .

$5 x + 7 = 0$

Solve $5 x + 7 = 0$ for $x$ .

Subtract $7$ from both sides of the equation.

$5 x = - 7$

Divide each term in $5 x = - 7$ by $5$ and simplify.

Divide each term in $5 x = - 7$ by $5$ .

$\frac{5 x}{5} = \frac{- 7}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 7}{5}$

Divide $x$ by $1$ .

$x = \frac{- 7}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{5}$

The final solution is all the values that make $x (5 x + 7) = 0$ true.

$x = 0, - \frac{7}{5}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- \frac{7}{5}, 0)$

Find the y-intercepts.

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

$y = \frac{5 {(0)}^{2} + 7 (0)}{2 {(0)}^{2} - 6 \cdot 0 - 80}$

Solve the equation.

Remove parentheses.

$y = \frac{5 \cdot 0^{2} + 7 (0)}{2 {(0)}^{2} - 6 \cdot 0 - 80}$

Remove parentheses.

$y = \frac{5 \cdot 0^{2} + 7 (0)}{2 \cdot 0^{2} - 6 \cdot 0 - 80}$

Remove parentheses.

$y = \frac{5 {(0)}^{2} + 7 (0)}{2 {(0)}^{2} - 6 \cdot 0 - 80}$

Simplify $\frac{5 {(0)}^{2} + 7 (0)}{2 {(0)}^{2} - 6 \cdot 0 - 80}$ .

Simplify the numerator.

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

$y = \frac{5 \cdot 0 + 7 (0)}{2 \cdot 0^{2} - 6 \cdot 0 - 80}$

Multiply $5$ by $0$ .

$y = \frac{0 + 7 (0)}{2 \cdot 0^{2} - 6 \cdot 0 - 80}$

Multiply $7$ by $0$ .

$y = \frac{0 + 0}{2 \cdot 0^{2} - 6 \cdot 0 - 80}$

Add $0$ and $0$ .

$y = \frac{0}{2 \cdot 0^{2} - 6 \cdot 0 - 80}$

Simplify the denominator.

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

$y = \frac{0}{2 \cdot 0 - 6 \cdot 0 - 80}$

Multiply $2$ by $0$ .

$y = \frac{0}{0 - 6 \cdot 0 - 80}$

Multiply $- 6$ by $0$ .

$y = \frac{0}{0 + 0 - 80}$

Add $0$ and $0$ .

$y = \frac{0}{0 - 80}$

Subtract $80$ from $0$ .

$y = \frac{0}{- 80}$

Divide $0$ by $- 80$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(0, 0), (- \frac{7}{5}, 0)$

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

Find the x and y Intercepts f(x)=(5x^2+7x)/(2x^2-6x-80)

Related Questions

Support LCMGCF.com by disabling your adblocker.