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The maximum.
Vertex
It is (y - b)^2 = ax + c
First you need more details about the parabola. Then - if the parabola opens upward - you can assume that the lowest point of the triangle is at the vertex; write an equation for each of the lines in the equilateral triangle. These lines will slope upwards (or downwards) at an angle of 60°; you must convert that to a slope (using the tangent function). Once you have the equation of the lines and the parabola, solve them simultaneously to check at what points they cross. Finally you can use the Pythagorean Theorem to calculate the length.
The vertex is not affected by the direction that the parabola is facing. The vertex is the place where the two sides of the parabola meet. It is in the middle divides the shape in half. If you picture yourself looking at a bowl from the side and then imagining it as two dimensional, it would look like a parabola but for all of the filled in parts of the graph and the fact that the sides of the bowl don't continue on forever. The vertex is the bottom of the bowl, where the sides meet. You measure a vertex as you would a point; with a coordinate.