Understanding the Parabola's Constants: a, b, c

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Homework Help Overview

The discussion revolves around understanding the units of the constants a, b, and c in the equation of a parabola, y=ax²+bx+c. Participants are exploring the implications of dimensional analysis in this context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the units of the constants, questioning why b is considered dimensionless and how the unit for a is derived as 1/m. There are discussions on ensuring that the units on both sides of the equation match, with some participants suggesting that the parabola may represent a physical scenario, such as free-fall.

Discussion Status

The discussion is active, with participants providing insights and asking for deeper explanations. Some have offered guidance on how to approach the unit analysis, while others are seeking further clarification on the reasoning behind the units assigned to each constant.

Contextual Notes

There is a mention of the need for units to match on both sides of the equation, and some participants express a lack of experience in physics, which may affect their understanding of the concepts being discussed.

mistalopez
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Homework Statement



The general equation for a parabola is y=ax²+bx+c, where a, b, c are constants. What are the units of each constant?

Homework Equations



y=ax²+bx+c

The Attempt at a Solution



The answer is a: 1/m; b: dimensionless; c: m

How exactly did they get that answer in the book? Can someone explain? I do not understand how b is dimensionless rather than a which is a fraction. Also, where did the 1/m come from?
 
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Hi mistalopez, welcome to PF.
y is the displacement which is measured in meter.
You must have the same unit in right hand side.
So ax^2 = 1/m*m^2
Similarly the other two.
 
rl.bhat said:
Hi mistalopez, welcome to PF.
y is the displacement which is measured in meter.
You must have the same unit in right hand side.
So ax^2 = 1/m*m^2
Similarly the other two.

Thanks for such a quick reply and the warm welcome! However, the answer flew way above my head. Would it be possible to explain it in more depth for someone who does not have much experience in physics to understand?
 
The units on both sides of the equation must match. So since y is in meters, (and I believe x is in meters) ax^2 must be in meters, and so on for the other two.

So, just for ax^2, you have meters squared times some unit gives meters. So, the unit for a must be inverse meters. I'll let you handle the other two.
 
First, the constants in a parabola equation have no units. A parabola is a mathematical construct, not a physical one, so it doesn't have units any more than the number 2.1 does.

Second, I suspect the parabola is supposed to represent a free-fall trajectory, where y represents height and x represents horizontal displacement. In that case, y must have units of meters, so ax^2, bx, and c must all have units of meters. Otherwise, you couldn't add them; what does it mean to add 2 m to 3 s, for example?

Since x must have units of meters, what must the units of "a" be to make ax^2 also have units of meters? How about bx?
 

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