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

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

Find the x-intercepts.

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

$0 = | 4 x + 2 | - 6$

Solve the equation.

Rewrite the equation as $| 4 x + 2 | - 6 = 0$ .

$| 4 x + 2 | - 6 = 0$

Add $6$ to both sides of the equation.

$| 4 x + 2 | = 6$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$4 x + 2 = \pm 6$

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.

$4 x + 2 = 6$

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$4 x = 6 - 2$

Subtract $2$ from $6$ .

$4 x = 4$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $4$ by $4$ .

$x = 1$

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

$4 x + 2 = - 6$

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$4 x = - 6 - 2$

Subtract $2$ from $- 6$ .

$4 x = - 8$

Divide each term in $4 x = - 8$ by $4$ and simplify.

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 8}{4}$

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

Simplify the right side.

Divide $- 8$ by $4$ .

$x = - 2$

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

$x = 1, - 2$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (- 2, 0)$

Find the y-intercepts.

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

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

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

Simplify each term.

Multiply $4$ by $0$ .

$y = | 0 + 2 | - 6$

Add $0$ and $2$ .

$y = | 2 | - 6$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$y = 2 - 6$

Subtract $6$ from $2$ .

$y = - 4$

y-intercept(s) in point form.

y-intercept(s): $(0, - 4)$

List the intersections.

x-intercept(s): $(1, 0), (- 2, 0)$

y-intercept(s): $(0, - 4)$

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

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