If the equation \(y = ax^2 + bx + c\) is a parabola, find the quadratic constant of variation if the vertex of the parabola is at (2, -3) and it passes through the point (4, 5).

Step 1 ：Step 1: Since the vertex form of a parabola is given by \(y = a(x - h)^2 + k\), where (h, k) is the vertex of the parabola, we can write the equation as \(y = a(x - 2)^2 - 3\).

Step 2 ：Step 2: Substitute the point (4, 5) into the equation to solve for 'a'. So, \(5 = a(4 - 2)^2 - 3 \Rightarrow 5 = 4a - 3\).

Step 3 ：Step 3: Solve the equation for 'a'. Add 3 to both sides, then divide by 4 to isolate 'a'. So, \(a = (5 + 3) / 4 = 2\).