Interpreting Quadratic Functions in Standard Form

The type of a quadratic functions' vertex is determined by the coefficient in front of the $x^2$-term. For the function $$y=2x^2-5x+4$$ 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 $x^2.$ Here it is $\text{-}8$, 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 $x^2$-term. This is because the function is linear. Linear functions does not have any vertex.

In $$y=x^2+7$$ there is an invisible $1$ in front of the $x^2$-term. The term can then be written as $1\cdot x^2.$ Since $1$ is a positive number, the curve looks like a happy mouth, and then has a minimum point.