# Purpose of coefficients in a equation or expression?

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.

* 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?

But how do I come up a number that is so precise like:

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?

Thanks!

#### Attachments

• equationthree_zpspxzjkzrv.png
4.5 KB · Views: 324
• coefficients_zpsfewsmrvs.png
23.1 KB · Views: 222
• Screenshot-2018-6-27%20Desmos%20Scientific%20Calculator2_zpsji2vfmgf.png
2 KB · Views: 164
• equation3_zpsysmqvhob.png
10.1 KB · Views: 163
jedishrfu

mfb
Mentor
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}##