Finding the Vertex of the Function f(x) = |x| – 2: Step-by-Step Guide with Calculation

What is the vertex of: f(x) = |x| – 2

(0, -2)

To find the vertex of the function f(x) = |x| – 2, we need to remember that the vertex represents the lowest or highest point of a graph.

In this case, the function f(x) = |x| – 2 is an absolute value function, which means it has a “V” shape. The vertex is the bottom point of this “V” shape.

To find the x-coordinate of the vertex, we set the expression inside the absolute value bars to zero, since that is where the vertex occurs. So we solve for x in the equation |x| – 2 = 0.

Adding 2 to both sides, we have |x| = 2.

Since an absolute value function can be positive or negative, we have two cases to consider:

Case 1: x is positive.
If x is positive, then the equation becomes x = 2.

Case 2: x is negative.
If x is negative, then the equation becomes -x = 2.
Solving for x by multiplying both sides by -1, we get x = -2.

Therefore, the x-coordinate of the vertex is x = 2 and x = -2.

To find the y-coordinate of the vertex, we substitute these x-values back into the original equation: f(x) = |x| – 2.

For x = 2: f(2) = |2| – 2 = 2 – 2 = 0.
For x = -2: f(-2) = |-2| – 2 = 2 – 2 = 0.

So, the y-coordinate of the vertex is 0.

Therefore, the vertex of the function f(x) = |x| – 2 is (2, 0) and (-2, 0).

More Answers:
Finding the Vertex of the Function f(x) = |x| – 4: Explained and Illustrated
Understanding the Vertex of Absolute Value Functions: Explained with f(x) = |x – 4|
Determining the Vertex of an Absolute Value Function: Understanding Horizontal Shifts | Math Tutorial

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