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

Coradossi7xod

Coradossi7xod

Answered question

2022-03-27

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

Answer & Explanation

zalutaloj9a0f

zalutaloj9a0f

Beginner2022-03-28Added 17 answers

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 "focus" and a line called the "directrix." 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't have a center that is the same distance from each of its points, it isn't a circle.
Curves such as y=x1.65, don't have a focus and directrix that behave the way a parabola'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't obvious. The answer below of Vítězslav Štembera says that the equation must have one of two specific forms, but that isn't correct. Any equation of the form
Ax2+2Bxy+Cy2+2Dx+2Ey+F=0
will have a parabolic graph, if it is non-degenerate and if ACB2=0. For example, if one takes the parabola y=x2 and rotates it by 45 the curve is still a parabola, with equation x22xy+y2x2y2=0.

Boehm98wy

Boehm98wy

Beginner2022-03-29Added 18 answers

A parabola is a form function (yy0)2=2p(xx0) or (xx0)2=2p(yy0) i.e. the quadratic term must be always present. y=x1.65 is not a parabola.

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