Given: y=x1.65Could it be described as parabolic in shape, or does the equation have to have x2 as its highest degree term?

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zalutaloj9a0f · Accepted Answer

Not all u-shaped objects are parabolas. A parabola has a highly peculiar shape and unique set of characteristics.Each point on a parabola, for instance, is the same distance from the focus as it is from the directrix because each parabola has a point called the &quot;focus&quot; and a line called the &quot;directrix.&quot; This is comparable to the way a circle has a center and all of its points are equally distant from it.A shape might look more or less circular, but if it doesn&#039;t have a center that is the same distance from each of its points, it isn&#039;t a circle.Curves such as&amp;nbsp;y=x1.65, don&#039;t have a focus and directrix that behave the way a parabola&#039;s do. They might look parabolic, but they are not parabolas.Note also that an equation may have a parabolic graph even if it isn&#039;t obvious. The answer below of Vítězslav Štembera says that the equation must have one of two specific forms, but that isn&#039;t correct. Any equation of the formAx2+2Bxy+Cy2+2Dx+2Ey+F=0will have a parabolic graph, if it is non-degenerate and if&amp;nbsp;AC−B2=0. For example, if one takes the parabola&amp;nbsp;y=x2&amp;nbsp;and rotates it by&amp;nbsp;45∘&amp;nbsp;the curve is still a parabola, with equation&amp;nbsp;x2−2xy+y2−x2−y2=0.

Boehm98wy · Accepted Answer

A parabola is a form function&amp;nbsp;(y−y0)2=2p(x−x0)&amp;nbsp;or&amp;nbsp;(x−x0)2=2p(y−y0)&amp;nbsp;i.e. the quadratic term must be always present.&amp;nbsp;y=x1.65&amp;nbsp;is not a parabola.

Given: \(\displaystyle{y}={x}^{{{1.65}}}\) Could it be described as parabolic

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