Students learn how a single “parent” function can be shifted, stretched, and flipped to create a whole family of graphs — mastering how the numbers in y = a(x − h)² + k move and reshape a parabola.
Students will be able to…
Every parabola is just y = x² in disguise — shifted, stretched, or flipped. What do the numbers h, k, and a each do to the graph?
Project this and change a, h, and k. Watch the parent parabola (gray) shift, stretch, and flip into the new graph (blue).
Tap any phase to open the teacher moves and student actions.
Every parabola is y = x² in disguise — how?
Teacher models.
Class uses the Transformation Grapher.
Students transform functions.
One transformation.
Aligned to the Common Core State Standards for Mathematics (High School: Algebra II).
Identify the effect of transformations on the graph of a function.
Graph functions and show key features.
Interpret key features of graphs.
Write a function that describes a relationship.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students apply the same shifts, stretches, and reflections to other parent functions (absolute value, square root, cubic). A printable transformations sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.