Find the x and y Intercepts y=-x(x+6)(3x-4)

$y = - x (x + 6) (3 x - 4)$

Step 1

Find the x-intercepts.

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

$0 = - x (x + 6) (3 x - 4)$

Solve the equation.

Rewrite the equation as $- x (x + 6) (3 x - 4) = 0$ .

$- x (x + 6) (3 x - 4) = 0$

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

$x = 0$

$x + 6 = 0$

$3 x - 4 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Set $3 x - 4$ equal to $0$ and solve for $x$ .

Set $3 x - 4$ equal to $0$ .

$3 x - 4 = 0$

Solve $3 x - 4 = 0$ for $x$ .

Add $4$ to both sides of the equation.

$3 x = 4$

Divide each term in $3 x = 4$ by $3$ and simplify.

Divide each term in $3 x = 4$ by $3$ .

$\frac{3 x}{3} = \frac{4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{4}{3}$

Divide $x$ by $1$ .

$x = \frac{4}{3}$

The final solution is all the values that make $- x (x + 6) (3 x - 4) = 0$ true.

$x = 0, - 6, \frac{4}{3}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- 6, 0), (\frac{4}{3}, 0)$

Step 2

Find the y-intercepts.

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

$y = 0 ((0) + 6) (3 (0) - 4)$

Solve the equation.

Remove parentheses.

$y = 0 (0 + 6) (3 (0) - 4)$

Remove parentheses.

$y = 0 ((0) + 6) (3 (0) - 4)$

Simplify $0 ((0) + 6) (3 (0) - 4)$ .

Add $0$ and $6$ .

$y = 0 \cdot 6 (3 (0) - 4)$

Multiply $0$ by $6$ .

$y = 0 (3 (0) - 4)$

Multiply $3$ by $0$ .

$y = 0 (0 - 4)$

Subtract $4$ from $0$ .

$y = 0 \cdot - 4$

Multiply $0$ by $- 4$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0), (- 6, 0), (\frac{4}{3}, 0)$

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

Step 4

Find the x and y Intercepts y=-x(x+6)(3x-4)

Related Questions

Support LCMGCF.com by disabling your adblocker.