Question

Vertex of y=|4x-1|

Answer 1

The vertex form of the absolute function is \(y=a|x-h|+k\), where the vertex is \((h, k)\). So you can transform what you have into the given form:
\(|4x-1|\\= \left|4\left(x-\dfrac{1}{4}\right) \right|\\
=4\left|x-\dfrac{1}{4} \right|\)

So you have that the vertex is \(\left( \frac{1}{4},0\right)\)

Answer 2

Hint: the x-coordinate of the vertex can be found by setting the quantity inside the absolute value operators equal to zero and solving for x. kirbykirby's approach is a very good one. My method will also give you x = 1/4.