The additional point here in this diagram is (0,c) which is very simple and easy to remember and there is no complication.
Whenever a quadratic cuts the y-axis it is always at this point (0,c)
Since the U is a symmetric diagram, it has an axis about which it is symmetric and this axis lies between the two roots alpha and beta and as we have seen earlier the axis is given as x= – b/2a.
So we can find any y point in a graph by putting the x value into the expression. That is precisely what has been done and shown in the diagram above and we get the result as (- D/4a).
A Diagram to embed in your mind
Commit this diagram into your mind, embed it graphically, understand it algebraically, see its constituent parts, see the Axis, the lowest point the distance between the mid point and alpha & beta, the minimum value of the quadratic. Do you see how many different facets of the quadratic now becomes clear?