Stop Guessing! Here’s How to Write the Equation from a Transformed Graph

Learn how to write the equation of a transformed parent function! This video breaks down the process of solving for the vertical stretch/shrink (a), horizontal shift (h), and vertical shift (k) for various common functions. Master how to go from a graph to its algebraic equation! In this tutorial, you will discover: Identifying Parent Functions: Recognize absolute value, square root, quadratic (parabola), and cubic graphs. Determining Shifts (H & K): How to find the horizontal (h) and vertical (k) shifts by locating the transformed vertex or key point. Solving for Stretch/Shrink (A): Using an additional given point on the graph to calculate the a value, which indicates vertical stretch, shrink, or reflection. General Forms: Understanding the general equation y = a * f(x - h) + k for different parent functions. We'll work through six detailed examples together, providing step-by-step guidance for each function type. Perfect for algebra and pre-calculus students looking to solidify their understanding of function transformations! Timestamps: 00:00 - Introduction: Writing Equations of Transformed Parent Functions 0:25 - Example 1: Absolute Value Function Transformation 0:50 - Identifying Parent Function and Shifts (H & K) 1:20 - Solving for 'A' using a Given Point 2:10 - Final Equation for Example 1 2:25 - Example 2: Square Root Function Transformation 2:50 - Identifying Parent Function, Reflection, and Shifts 3:20 - Solving for 'A' for the Square Root Function 4:10 - Final Equation for Example 2 4:25 - Example 3: Quadratic Function Transformation (Vertex Form) 4:50 - Identifying Parent Function and Vertex Shift 5:20 - Solving for 'A' for the Quadratic Function 6:00 - Final Equation for Example 3 6:20 - Example 4: Cubic Function Transformation 6:50 - Identifying Parent Function and Point of Inflection Shift 7:15 - Solving for 'A' for the Cubic Function 8:10 - Final Equation for Example 4 8:25 - Example 5: Another Absolute Value Function Transformation 8:50 - Identifying Vertex Shift (H & K) 9:15 - Solving for 'A' for the Second Absolute Value Function 10:00 - Final Equation for Example 5 10:20 - Example 6: Modified Square Root Function Transformation 10:50 - Identifying Parent Function and Key Point Shift 11:15 - Solving for 'A' for the Modified Square Root Function 12:00 - Final Equation for Example 6 Don't forget to like, comment, and subscribe for more math tutorials! #FunctionTransformations #ParentFunctions #AlgebraHelp #PreCalculus #GraphingFunctions #EquationWriting #MathTutorial #VertexForm ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos)    / @mariosmathtutoring