Question

What is the vertex of the absolute value function below? (4, –1) (1, –4) (1, 4) (4, 1)

Answer 1

The correct answer is: (4,1)

Explanation:

First let me explain you what a vertex is (in non-bookish terms).

(In simple words) Vertex is a (common) point where two rays or line segments meet. This definition holds when we talk about straight lines (while looking at the graph). In the graph of absolute valued function attached with the question, you can see there are two lines, one going up (increasing) and the other going down (decreasing), and both meet at x = 4. Now look at the value of y at x = 4. It is +1. In other words, you can say that at x = 4, there is a transition in a graph.

Therefore, the vertex of the absolute value function is (4, 1).

Information: The definition of vertex totally changes when we talk about parabola, or any non-linear equation. In that case, the vertex is the peak value of the graph (where there is a transition). The peak could be positive or negative depending upon the graph or equation; however, in the case of straight lines, adhere to what I explained above. Goodluck!

-i