First you have to identify the values of a, b, and c of the given quadratic equation in the general form:
ax² + bx + c = 0
vertex is (h, k)
h = -b/2a
k = 4ac -b²
h is x coordinate, and k is the y-coordinate of the vertex (h, k).
Note that if the parabola (graph of the quadratic equation) opens downward (inverted U), the vertex is the maximum. While if the parabola opens upward (U-shaped), the vertex is the minimum.
To know without graphing if the parabola opens downward, a is negative; opens upward, a is positive.