What is the vertex of: f(x) = |x – 2|
(2, 0)
To find the vertex of a function in the form f(x) = |x – a|, we need to first determine the value of “a”. In this case, “a” represents the horizontal shift of the absolute value function.
Looking at the function f(x) = |x – 2|, we can see that “a” is equal to 2. This means that the graph of our function will be shifted 2 units to the right.
The vertex of an absolute value function in the form f(x) = |x – a| can be found by considering two cases:
Case 1: When x < a In this case, |x - a| simplifies to -(x - a), resulting in f(x) = -(x - a). Case 2: When x ≥ a In this case, |x - a| remains as it is, f(x) = |x - a|. In both cases, x - a represents the distance between x and a on the number line. The vertex of the function occurs at the point (a, 0). So, in our case, the vertex of f(x) = |x - 2| is (2, 0). This means that the graph of the function is shifted 2 units to the right with the lowest point (vertex) at (2, 0).
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