The vertex, the quadratic minimum and the quadratic maximum are also helpful when answering problems associated with area, speed and direction. We find the minimum if the parabola opens up and the maximum if the parabola opens down.. maximum max minimum min vertex quadratic. So, hopefully by now, you are comfortable with the fact that ax squared plus bx plus c is the graph of a parabola. OK, the A determines what the graph is facing, up or down.