The normal equations discussed in this paper for a least-squares parabolic fit have a unique solution if and only if there are at least three different x-values in the observations. This requirement is satisfied by most real sets of quantitative observations. For particular data sets, the appropriateness of parabolic fits should be assessed with scatter plots, correlation coefficients, and residual analyses. An additional benefit of rewriting the sums in this way is that the determinant, which appears in the solution of the normal equations, is expressed in a way that can simplify calculations.