Find the x and y Intercepts f(x)=2x(4x+1)(x-6)

$f (x) = 2 x (4 x + 1) (x - 6)$

Step 1

Find the x-intercepts.

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

$0 = 2 x (4 x + 1) (x - 6)$

Solve the equation.

Rewrite the equation as $2 x (4 x + 1) (x - 6) = 0$ .

$2 x (4 x + 1) (x - 6) = 0$

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

$x = 0$

$4 x + 1 = 0$

$x - 6 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $4 x + 1$ equal to $0$ and solve for $x$ .

Set $4 x + 1$ equal to $0$ .

$4 x + 1 = 0$

Solve $4 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$4 x = - 1$

Divide each term in $4 x = - 1$ by $4$ and simplify.

Divide each term in $4 x = - 1$ by $4$ .

$\frac{4 x}{4} = \frac{- 1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 1}{4}$

Divide $x$ by $1$ .

$x = \frac{- 1}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{4}$

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

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

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

The final solution is all the values that make $2 x (4 x + 1) (x - 6) = 0$ true.

$x = 0, - \frac{1}{4}, 6$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- \frac{1}{4}, 0), (6, 0)$

Step 2

Find the y-intercepts.

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

$y = 2 (0) (4 (0) + 1) ((0) - 6)$

Solve the equation.

Remove parentheses.

$y = 2 (0) (4 (0) + 1) (0 - 6)$

Remove parentheses.

$y = 2 (0) (4 (0) + 1) ((0) - 6)$

Simplify $2 (0) (4 (0) + 1) ((0) - 6)$ .

Multiply $2$ by $0$ .

$y = 0 (4 (0) + 1) ((0) - 6)$

Multiply $4$ by $0$ .

$y = 0 (0 + 1) ((0) - 6)$

Add $0$ and $1$ .

$y = 0 \cdot 1 ((0) - 6)$

Multiply $0$ by $1$ .

$y = 0 ((0) - 6)$

Subtract $6$ from $0$ .

$y = 0 \cdot - 6$

Multiply $0$ by $- 6$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0), (- \frac{1}{4}, 0), (6, 0)$

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

Step 4

Find the x and y Intercepts f(x)=2x(4x+1)(x-6)

Related Questions

Support LCMGCF.com by disabling your adblocker.