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

$f (x) = 3 | x + 4 | - 4$

Step 1

Find the x-intercepts.

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

$0 = 3 | x + 4 | - 4$

Solve the equation.

Rewrite the equation as $3 | x + 4 | - 4 = 0$ .

$3 | x + 4 | - 4 = 0$

Add $4$ to both sides of the equation.

$3 | x + 4 | = 4$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $| x + 4 |$ by $1$ .

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

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

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

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.

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

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

Subtract $4$ from both sides of the equation.

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

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Combine $- 4$ and $\frac{3}{3}$ .

$x = \frac{4}{3} + \frac{- 4 \cdot 3}{3}$

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 4$ by $3$ .

$x = \frac{4 - 12}{3}$

Subtract $12$ from $4$ .

$x = \frac{- 8}{3}$

Move the negative in front of the fraction.

$x = - \frac{8}{3}$

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

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

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

Subtract $4$ from both sides of the equation.

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

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Combine $- 4$ and $\frac{3}{3}$ .

$x = - \frac{4}{3} + \frac{- 4 \cdot 3}{3}$

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 4$ by $3$ .

$x = \frac{- 4 - 12}{3}$

Subtract $12$ from $- 4$ .

$x = \frac{- 16}{3}$

Move the negative in front of the fraction.

$x = - \frac{16}{3}$

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

$x = - \frac{8}{3}, - \frac{16}{3}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{8}{3}, 0), (- \frac{16}{3}, 0)$

Step 2

Find the y-intercepts.

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

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

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

Simplify each term.

Add $0$ and $4$ .

$y = 3 | 4 | - 4$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$y = 3 \cdot 4 - 4$

Multiply $3$ by $4$ .

$y = 12 - 4$

Subtract $4$ from $12$ .

$y = 8$

y-intercept(s) in point form.

y-intercept(s): $(0, 8)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{8}{3}, 0), (- \frac{16}{3}, 0)$

y-intercept(s): $(0, 8)$

Step 4

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

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