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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:

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