Abstract
In this paper, we investigate the proper shape and location of the maximum curve of transcendental entire functions <TEX>$e^{az^2+bz+c}$</TEX>. We show that the alpha curve of <TEX>$e^{az^2+bz+c}$</TEX> is a subset of a rectangular hyperbola, and the maximum curve is the connected set originating from the origin as a subset of the alpha curve.
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