Q: Why are parabolas important?

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yes

Parabolas have directori.

McDonalds Arches

There are two ways of classifying parabolas: By the direction in which they are open: open at the top or at the bottom. By the number of real roots: 2 real, 1 real or no real roots.

The form is not specified in the question so it is hard to tell. But two parabolas with different vertices can certainly have the same axis of symmetry.

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Becuase a parabola is an arch shape so that is why the 'golden arches' are parabolas.

NO. They do not oscillate.

yes

hyperbolas have an eccentricity (fixed point to fixed line ratio) that is greater than 1, while the parabolas have an exact eccentricity that is equal to 1. And hyperbolas are always come in pairs while parabolas are not.

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Parabolas have directori.

When a comet has an orbit that is a parabola it never returns. This is because parabolas never meet in the same place that they start.

Parabolas are used in real life in light reflectors on cars to create a concentrated beam of intense light. Braking distance and stopping distance are quadratic formulas so their graphs are parabolas. A ball in motion in space has a path of a parabola.

McDonalds Arches

--actually they are used in real life. parabolas are seen in "parabolic microphones" or satellites. and there are others for both ellipses and hyperbolas.

There are two ways of classifying parabolas: By the direction in which they are open: open at the top or at the bottom. By the number of real roots: 2 real, 1 real or no real roots.

The form is not specified in the question so it is hard to tell. But two parabolas with different vertices can certainly have the same axis of symmetry.