If the number in front of the x squared is negative, then the parabola will open upwards. The opposite occurs when the number is positive.
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The extreme point it the highest or lowest point of the parabola (depending if it is concave downwards or upwards). It is the point of the parabola tat is closest to the focus. the extreme point lies on the axis of symmetry.
Finding the vertex of the parabola is important because it tells you where the bottom (or the top, for a parabola that 'opens' downward), and thus where you can begin graphing.
Opening up, the vertex is a minimum.
open upward
A parabola that opens upward is a U-shaped curve where the vertex is the lowest point on the graph. It can be represented by the general equation y = ax^2 + bx + c, where a is a positive number. The axis of symmetry is a vertical line passing through the vertex, and the parabola is symmetric with respect to this line. The focus of the parabola lies on the axis of symmetry and is equidistant from the vertex and the directrix, which is a horizontal line parallel to the x-axis.