How do you find the x intercept of absolute value

To find the \( x \)-intercept of an absolute value function, you follow these steps:

### 1. **Set the Function Equal to Zero**:
   The \( x \)-intercept is where the function crosses the \( x \)-axis, meaning the output (or \( y \)-value) is zero. For an absolute value function \( y = |f(x)| \), set the function equal to zero:
   \[
   |f(x)| = 0
   \]

### 2. **Solve the Equation Inside the Absolute Value**:
   The absolute value of a number is zero only when the number itself is zero. So, solve the equation inside the absolute value for \( x \):
   \[
   f(x) = 0
   \]

### 3. **Determine the \( x \)-Intercept**:
   Solve the equation \( f(x) = 0 \) to find the value(s) of \( x \). The solution(s) will be the \( x \)-intercept(s) of the absolute value function.

### Example:
Let's consider the function \( y = |2x - 4| \).

1. Set the function equal to zero:
   \[
   |2x - 4| = 0
   \]
   
2. Solve the equation inside the absolute value:
   \[
   2x - 4 = 0
   \]

3. Solve for \( x \):
   \[
   2x = 4
   \]
   \[
   x = 2
   \]

The \( x \)-intercept is at \( x = 2 \). So, the \( x \)-intercept is the point \( (2, 0) \).

Would you like more details on this process or have any further questions?

Here are 5 related questions you might consider:

1. How do you graph an absolute value function and identify its vertex?
2. What happens to the graph of an absolute value function when you change its coefficients?
3. How do you find the vertex of an absolute value function?
4. Can an absolute value function have more than one \( x \)-intercept?
5. How do you solve absolute value inequalities?

**Tip:** When solving absolute value equations, always consider checking for extraneous solutions, especially if the equation involves squaring both sides.

How do you find the x intercept of absolute value?

Learn how to find the x-intercept of an absolute value function, with a step-by-step solution. This example uses the function |2x - 4| and includes solving the equation inside the absolute value and identifying the x-intercept. Suitable for students in Grades 8-10.

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