The type of a quadratic functions' vertex is determined by the coefficient in front of the x2-term. For the function y=2x2−5x+4 it is 2, positive. This means that the curve looks like a happy mouth, and, thus, it's an absolute minimum.
Again, look at the coefficient in front of x2. Here it is -8, so negative, which means that the curve has the shape of an sad mouth, which means it has an absolute maximum.
In this function, there is no x2-term. This is because the function is linear. Linear functions does not have any vertex.
In y=x2+7 there is an invisible 1 in front of the x2-term. The term can then be written as 1⋅x2. Since 1 is a positive number, the curve looks like a happy mouth, and then has a minimum point.