This paper discusses a problem in the spacing of observations in quadratic regression for most precise extrapolation. LetE(yi) = α + βxi+ γxi2. Theyiare uncorrelated observations with varianceVo;thexiare controlled. The problem answered is: at whichx-values in a specified interval [xL, xH] shouldNobservationsyi, i= 1 (1)N, be taken so that for a ξ >xH(or ξ <xL) the least squares estimate of α + βξ + γξ2has minimum variance? It is shown that the observations are located atxL, (xL+ xH)/2, andxH.The distribution at these locations as a function of ξ is given. These results are also useful in designing experiments for testing the hypothesis of a quadratic relation versus that of a linear relation.