Interpolation: Linear to Quadratic with Python | Ancient Secrets of Prediction | Linear Algebra #3

Welcome to the third video in the Ancient Secrets of Prediction series! In this video, we dive into Quadratic Interpolation — building on the concepts of linear equations discussed in the previous parts. Quadratic interpolation is a method used to estimate values between known data points by fitting a quadratic (parabolic) curve through them. We break down how interpolation evolves from linear to quadratic, explaining the math behind it and visualizing the process step by step. We also bring these concepts to life using Python — walking through the code clearly so you understand every line and how it translates math into motion. Our goal is to make Machine Learning intuitive and fun by tracing its roots back to basic mathematics and illustrating complex ideas with engaging animations. These animations are generated by a Python library called "Manim". 0:00 Introduction 0:08 Recap 1:01 Quadratic Interpolation 1:22 Website Traffic Analogy 1:39 Time Traffic Equations 3:32 Calculating Coefficients 4:14 Matrices 4:58 Vectors 5:44 Matrix Multiplication 6:49 Multiply Vectors Code 8:30 Degree of Polynomial Examples 9:53 Intro to code automation 12:01 Previous Code Recap 12:40 Code to Automate 12:58 Step 1: Equations to Matrix 16:29 Step 2: Extract coefficients from matrix 16:42 Step 3: Prepare polynomial equation 17:55 Step 4: Multiply vectors 18:41 Questions 18:49 Summary 🎬 Video credits: Nikita Bhagat (LinkedIn- https://in.linkedin.com/in/nikitabhagat-nb), Here is the link for Ancient Secrets of Prediction Git repository -https://github.com/girisandeep/asop Here is the link for Git repository -https://github.com/cloudxlab Drop us a mail at reachus@cloudxlab.com in case of any query. To know more about CloudxLab visit - https://cloudxlab.com/ Follow us on social media for the latest updates- Facebook- https://www.facebook.com/cloudxlab/ Instagram- https://www.instagram.com/cloudxlab Twitter- https://www.twitter.com/cloudxlab LinkedIn- https://www.linkedin.com/co