Locus of Vertex

Geometry Level pending

Consider the family of parabolas whose equations have the form \[ y = x^2 - 2px + 3p^2 - 5p, \] where \(p\) is a real number. The loci of the vetices of these parabolas satisfy the equation \( y = f(x) \). Then what is \( f(7) ?\)

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