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Geometry Level 2

The equation of a curve can be written as \(y=ax^2+b\) where \(a\) and \(b\) are constants.

Point \(A,B\) and \(C\) lie on the curve.

Given that
point \(A\) has coordinates \((2,11)\),
point \(B\) has coordinates \((0.5,3.5)\), and
point \(C\) lies on the \(y\)-axis.

Find the \(y\)-coordinate of the point \(C\).


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