Problem: Quadratic functions and vertex

Problem

For a quadratic function with \(a>0\) , the bottom of the valley is called the vertex of the function. The \(y\) -coordinate of the vertex is the minimum value the function can take.

Similarly, for a quadratic function with \(a<0\) , the top of the hill is also a vertex. The \(y\) -coordinate of the vertex is here the maximum value the function can take. Find the vertex ( \(x\) - and \(y\) - coordinate) for the following quadratic functions:

1. \(y=x^2\)
2. \(y=-x^2\)
3. \(y=x^2+3\)