Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.
Compare linear and quadratic graphs by key features
Problem
Compare \(L(x)=3x+2\) and \(Q(x)=x^{2}\) on all real inputs.
Big Picture
What this problem is really about
Comparing function families means looking beyond a shared intercept or coefficient. We’ll classify each rule by degree, identify its key graph features, and compare how outputs change over equal input steps. The decisive contrast is whether first differences remain constant or change, which also explains why one graph keeps a single slope while the other bends, has symmetry, and can turn at an extremum.
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