Bifurcation of limit cycles in piecewise quadratic differential systems with an invariant straight line

We solve the center-focus problem in a class of piecewise quadratic polynomial differential systems with an invariant straight line. The separation curve is also line which not invariant. provide families having at origin weak-foci maximal order. In continuous class, cyclicity solved, being 3 such number. Moreover, for discontinuous but without sliding segment, we prove existence 7 limit cycles small amplitude.