Find the Vertex
First, we’ll work on the vertex. The vertex x-coordinate is given by x=h=-b/(2a). Recall that when in standard form, the convention is to use coefficients a, b, and c as in ax²+bx+c. Thus, a=1, b=-6, and c=15 in our example, and the x-coordinate of the focus is:
x = -b / (2a) = – (-6) / (2*1) = 6/2 = 3.
To find the y-coordinate of the vertex, k, we can either use the formula (4ac-b²)/(4a) in Figure B or plug the x-coordinate we found into y=ax²+bx+c. We’ll do the latter, using x=3 we just found:
y = ax² + bx + c = 1*(3)² – 6 (3) + 15 = 9 – 18 + 15 = 6.