Maths ( Functions and Graphs )

For a standard quadratic equation ax^2 + bx + c = 0, the x - coordinate of the vertex is - b/2a, so for this equation, it is - (4p)/(-4) = p. Since x - coordinate of the vertex = 3, so p = 3.
Co-ordinates of the vertex is (3, 15), sub. this point and p = 3 into the function, we get
15 = - 2(3^2) + 4(3)(3) + q
15 = - 18 + 36 + q
so q = - 3.

2011-07-19 07:48:32 補充：
Note : In exam., if the question is given in the form y = ax^2 + bx + c and you are not asked to transform to the form y = a(x - h)^2 + k first, using this method could be faster. Vertex is ( - b/2a, - delta/4a).

y=-2(x^2)+4px+q
y=-2[(x-p)^2]+2(p^2)+q since the axis of symmetry of the graph of the function
y= -2x^2 + 4px + q is x=3,
p=3 when x=p=3,
y is maximum
and y=2(p^2)+q=15
2(3^2)+q=15
18+q=15
q=-3