The present paper is devoted to the study of the maximum number of limitcycles bifurcated from the periodic orbits of the quadratic isochronous center$\dot{x}=-y+\frac{16}{3}x^{2}-\frac{4}{3}y^{2},\dot{y}=x+\frac{8}{3}xy$ by theaveraging method of first order, when it is perturbed inside a class ofdiscontinuous quadratic polynomial differential systems. The \emph{Chebyshevcriterion} is used to show that this maximum number is 5 and can be realizable.The result and that in paper \cite{LC} completely answer the questions left inthe paper \cite{LM}.
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