Lesson Plan

Identify all four parameters $a$, $b$, $h$, $k$ in an equation of the form $y = a,f(b(x-h)) + k$ and state each one's effect

Write the equation for a parent function subjected to a specified sequence of transformations

Apply transformations in the correct order to sketch a transformed graph, and explain why the order matters

Rewrite $y = f(bx - c)$ as $y = f(b(x-h))$ in order to read the horizontal shift correctly

Apply the composite point-mapping rule $(p, q) \mapsto \left(\frac{p}{b} + h,\ aq + k\right)$ to find the image of a named point

Identify characteristics — vertex, opening direction, width, intercept count — from a fully transformed equation

AF 706. Given an equation or function, find an equation or function whose graph is a translation by specified amounts in the horizontal and vertical directions AF 705. Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c AF 703. Analyze and draw conclusions based on properties of algebra and/or functions AF 604. Given an equation or function, find an equation or function whose graph is a translation by a specified amount up or down