Extremum-seeking (also peak-seeking) controllers are designed to operate at an a priori unknown set-point that extremizes the value of a performance function. Traditional approaches to the problem assume a time-scale separation between the gradient computation and function minimization and the system dynamics. The work here, in contrast, assumes that the performance function can be approximated by a quadratic function with affinite number of parameters. These parameters are estimated on-line and the extremum seeking controller operates based on these estimated values. A significant advantage of a quadratic function is that it allows the peak-seeking control loop to be reduced to a linear system. For such a loop, the wealth of linear system analysis and synthesis tools can be employed. First, the control loop is analysed assuming that the parameters in the function are known ( full information case) and then when the parameters are estimated on line (the partial information case).