Curve creation including y variable

I have this script:

from manimlib.imports import *
import numpy as np 

class graphx(GraphScene):
	CONFIG={
		"x_min": -4,
		"x_max": 4,
		"y_min": -2,
		"y_max": 2,
		"x_axis_label": "$x$",
		"y_axis_label": "$y$",
		"graph_origin": 0.5 * DOWN + 0 * LEFT,
	}

	# Defining graph functions 
	def show_function_graph(self): 
		self.setup_axes(animate=True)
		# Math function
		def func(x):
			return x**3 + 497*x + 1768
		#sin graph
		graph_sin=self.get_graph(func,x_min=-5, x_max=5)
		graph_sin.set_color(RED)
		# Cos graph

		
		# Play grapgs
		self.play(ShowCreation(graph_sin,), run_time=3)
		self.wait(1)
		# self.play(ShowCreation(graph_cos), run_time=3)



	# Defining construction
	def construct(self):
		self.show_function_graph()

and what I am trying to do is to show this curve: y^2 = x^3 + 497*x + 1768. Have tried to math.sqrt(x**3 + 497*x + 1768), but it doesn’t work. Is there any way that I can include y variable?

[NeoPlato]

Mate

Push the code block containing the method implicit curve one level of indentation lower. The way I see it you’ve placed it in the construct block hence it couldn’t be initialized as an attribute of the scene class.

[NeoPlato]

Your dilemma needs some serious math to be solved. Let’s dive in.

We start off by admitting that computers exist and if you’re going to hassle a graph in Manim at least get some help. Say, Desmos for example.

Your example is wayyy too complicated so I’m shrinking it down a bit.

Great! Now let’s think through this a bit.

For any x value you give me, can I determine the y value that is on that graph? Let’s see!

Yes…and no. Not all x values work(orange line) and even for those that do(purple line) you have to account for two solutions which is not very helpful.

The reverse is feasible though. Any y value gives you one and only one x value, Except it pushes you to do something less efficient and objectively worse: solving this equation:

x**3 + 2x + 1 = something

And not just for any specific something, which is doable by hand, but every point in the y range available. The good thing about this, however, is being able to represent that as a parametric equation which is already Manim programmed.

This is a good time to tell you that Desmos is an already existing and very awesome graphing calculator and for this case using Manim is overkill. But you asked the question and I have decided to answer.

You tell me if that’s worth the effort.