Purpose of coefficients in a equation or expression?

In summary, the conversation discusses the use of coefficients in an equation found on a website. The coefficients of x2 are used to scale the size of a shape drawn on the graph, but the precise value of the coefficient can be determined by solving an equation to ensure the curve is continuous.
  • #1
Hello.
I have an equation which I understand partially but after understanding the purpose of coefficients in the below equation I think my understanding will enhance.
equationthree_zpspxzjkzrv.png


* I found it on: https://www.desmos.com/calculator/dnzfajfpym

What decides that I need coefficients for x2 in the given equation of this post?

I think that coefficients of x2 in this post's equation exist to scale up or scale down the size of the thing drawn in blue box: Correct?

coefficients_zpsfewsmrvs.png


But how do I come up a number that is so precise like:
Screenshot-2018-6-27%20Desmos%20Scientific%20Calculator2_zpsji2vfmgf.png

which is the coefficient of x2 to complete the sketching of the curve (Batman)?

Do I need to solve a few equations to come up with the coefficient of x2 in the following equation?
equation3_zpsysmqvhob.png


Thanks!
 

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  • #2
pairofstrings said:
Do I need to solve a few equations to come up with the coefficient of x2 in the following equation?
Just one. It should match the elliptic parts outside: At ##x = \pm 4## the value of the function has to be about -2.45 to make the curve continuous. You can get the exact value from curve 2: It has to be ##-3\sqrt{1-(4/7)^2}##
 

1. What is the purpose of coefficients in an equation or expression?

Coefficients in an equation or expression are numerical constants that multiply a variable or term. They allow us to quantify the relationship between variables and determine the magnitude of change in the output based on changes in the input.

2. How do coefficients affect the graph of an equation?

The coefficient of a variable affects the slope of the graph of an equation. A larger coefficient results in a steeper slope, indicating a greater change in the output for a given change in the input. A negative coefficient will result in a downward slope, while a positive coefficient will result in an upward slope.

3. Can coefficients be negative?

Yes, coefficients can be negative. A negative coefficient indicates an inverse relationship between the variables. For example, if the coefficient of x is -2, then as x increases, y will decrease by twice the amount of x.

4. Are coefficients always whole numbers?

No, coefficients can be any real number, including fractions or decimals. They can also be irrational numbers, such as pi or square root of 2, depending on the context of the equation or expression.

5. How do you solve for coefficients in an equation or expression?

To solve for coefficients, you must have at least two equations or expressions with the same variables. You can then use algebraic methods, such as substitution or elimination, to isolate and solve for the coefficients. Additionally, in some cases, the coefficients may have a specific meaning or value based on the context of the problem or experiment.

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