To find the quadratic function f passing through the points (1,3) and (?2,6) with an axis of symmetry at x=2, we can use the standard form of a quadratic function: .First, let's use the points (1,3) and (?2,6) to form two equations:For point (1,3):
(equation 1)For point (?2,6):
(equation 2)Since the axis of symmetry is x=2, we know that the vertex of the parabola is at (2,k). The x-coordinate of the vertex can be found using the formula In this case, x=2, so we have: equation 3)Now, let's solve these equations to find the values of a, b, and c:From equation 3, we can rearrange it to find b: