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

  • Thread starter mistalopez
  • Start date
  • Tags
    Constants
In summary: The units of "a" and "b" are both 1/m, so the units of ax^2 are also 1/m. The unit for c is not given, but it must be the same as the units of "a" and "b".
  • #1
mistalopez
16
0

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?
 
Physics news on Phys.org
  • #2
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.
 
  • #3
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?
 
  • #4
The units on both sides of the equation must match. So since y is in meters, (and I believe x is in meters) [tex]ax^2[/tex] 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.
 
  • #5
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?
 

What is the significance of the constant "a" in a parabola?

The constant "a" in a parabola is known as the leading coefficient and determines the direction and shape of the parabola. A positive value of "a" will result in a parabola opening upwards, while a negative value will result in a parabola opening downwards.

What does the constant "b" represent in a parabola?

The constant "b" in a parabola is known as the linear coefficient and determines the position of the parabola's vertex. It also affects the direction of the parabola's opening, as a larger value of "b" will result in a narrower parabola.

How does the constant "c" impact a parabola?

The constant "c" in a parabola is known as the constant term and determines the vertical translation of the parabola. It shifts the entire parabola either up or down, depending on the value of "c".

Can the constants "a", "b", and "c" be changed without affecting the shape of the parabola?

No, the constants "a" and "b" directly impact the shape and position of the parabola, while "c" affects its translation. Changing any of these constants will result in a different parabola.

How do the constants "a", "b", and "c" relate to the quadratic formula?

The constants "a", "b", and "c" are used in the quadratic formula to solve for the roots of a parabola, which are the points where the parabola intersects the x-axis. The values of "a", "b", and "c" are substituted into the formula to find the x-values of the roots.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
770
  • Introductory Physics Homework Help
Replies
17
Views
310
Replies
19
Views
725
  • Introductory Physics Homework Help
Replies
3
Views
368
  • Introductory Physics Homework Help
Replies
1
Views
905
  • Precalculus Mathematics Homework Help
Replies
5
Views
683
  • Introductory Physics Homework Help
Replies
11
Views
3K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
910
Back
Top