Algebra and Quadratic Equations for Data Science Graphing
Master algebraic principles and quadratic equations to unlock powerful data modeling and visualization techniques for data science applications.
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Algebraic Foundations for Data Science
Unit 1: Variables, Expressions, and Equations
Algebraic Building Blocks
Data Types as Variables
Expressions in Data
Equations in Data Analysis
Unit 2: Data Structures and Algebraic Perspective
Lists as Variable Sets
Arrays: Ordered Data
Matrices: Data Tables
Unit 3: Order of Operations and Simplification
PEMDAS/BODMAS in Data
Simplifying Expressions
Distribution in Data
Unit 4: Functions and Data Relationships
What is a Function?
Function Notation
Types of Functions
Functions in Python
Linear Equations and Data Transformation
Unit 1: Solving Linear Equations
Review: Linear Equations
Solving for x
Equations with Fractions
Equations with Decimals
Word Problems
Unit 2: Linear Inequalities and Data Ranges
Intro to Inequalities
Solving Inequalities
Compound Inequalities
Inequalities in Data
Unit 3: Linear Transformations and Data
Slope-Intercept Form
Point-Slope Form
Linear Transformations
NumPy for Transformations
Modeling Relationships
Introduction to Quadratic Equations
Unit 1: Understanding Quadratic Equations
What are Quadratics?
Real-World Quadratics
Prep for Solving
Unit 2: Solving Quadratic Equations by Factoring
Factoring: The Basics
Factoring: Examples
Factoring: Special Cases
Unit 3: Completing the Square
Completing the Square
Completing the Square: 2
Unit 4: The Quadratic Formula
The Formula Revealed
Formula: Examples
Discriminant: Intro
Discriminant: Examples
Unit 5: Applications and Advanced Techniques
Data Analysis
Choosing Your Method
Quadratic Functions and Their Graphs
Unit 1: Graphing Basics and Key Features
Intro to Quadratic Graphs
The Vertex Explained
Axis of Symmetry
X and Y Intercepts
Graphing from Features
Unit 2: Equation and Graph Relationship
Standard Form Deep Dive
Vertex Form Explained
Factored Form Insights
Form Conversions
Equation to Graph
Unit 3: Parameter Effects and Applications
Impact of 'a' Value
Impact of 'b' Value
Impact of 'c' Value
Max/Min Applications
Modeling Non-Linear Data with Quadratic Equations
Unit 1: Introduction to Non-Linear Modeling
Why Not Just Linear?
Non-Linearity Examples
Intro to Polynomials
Unit 2: Quadratic Equations for Data Modeling
Quadratic Equations
Data Modeling
Polynomial Regression
Unit 3: Implementing Quadratic Regression
Python: Setup
Python: Model Training
Python: Visualization
Unit 4: Evaluating and Interpreting Quadratic Models
Goodness of Fit
Interpreting a, b, c
Overfitting?
Unit 5: Comparing Models
Linear vs. Quadratic
Beyond Quadratic
Visualizing Quadratic Functions in Data Analysis
Unit 1: Setting Up Your Visualization Environment
Python for Visualization
Jupyter Notebooks
First Plot: The Basics
Unit 2: Visualizing Quadratic Functions
Graphing Quadratics
Vertex on the Graph
Axis of Symmetry
Finding Intercepts
Unit 3: Advanced Visualization Techniques
Scatter Plots
Customizing Aesthetics
Seaborn's Magic
Annotations
Unit 4: Data-Driven Storytelling
Interpreting Graphs
Real-World Examples
Presenting Insights