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MCR3U Full Interactive Course

Ontario Grade 11 Functions (MCR3U) • interactive lessons with visuals, formulas, and quick checks

Visited 1 / 10 lessons

Explore Transformations of a Function

The controls and visual below help you build strong graph intuition. Start by moving the parabola, then continue through the full MCR3U course menu on the left.

Current lesson
1.1 Transformations
Main skill
Graph shifts and shape changes
Visual focus
Live graph updates
Practice type
Quick multiple choice
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Concept

Short explanation in student-friendly language.

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Interactive

Change variables and see the result instantly.

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Quick Check

Answer a review question and get instant feedback.

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Study Smart

Look for patterns first, then memorize formulas only after the idea makes sense.

Explore the interactive model

1.1 Transformations

In vertex form, y = a(x − h)² + k. The value of a changes the shape and direction, h moves the graph left or right, and k moves it up or down.

Big idea
Functions can be transformed in predictable ways.
Study move
Say the effect of each parameter out loud while moving the slider.
y = 1(x − 0)² + 0
What to notice
The vertex is the turning point. Reflection happens when a is negative.
Current output
Vertex: (0, 0)
Direction: opens up
Quick check & teacher tips

Quick check

If the vertex form is y = (x − 3)² + 2, what is the vertex?

Formula / rule
Vertex form: y = a(x − h)² + k
How to remember it
Think “shape, sideways, up/down”: a changes shape, h changes horizontal position, and k changes vertical position.
Exam hints
  • Always identify the form of the equation first.
  • State what each parameter does before solving.
  • Check if a negative sign changes the graph direction.
After-class practice

After-class practice

Question 1 of 10 Score 0 / 0

Work through all ten at your own pace. Pick an answer to see a worked solution, then use Previous / Next to move around. Reset clears your answers.

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Short-answer practice

Short-answer practice

Write, then reveal the answer key

Open-response questions — work them out on paper or in the box, then reveal the answer key to compare. Nothing here is auto-marked.

Lesson notes & worked examples

Lesson notes

MCR3U interactive study companion • Move the sliders, predict what will happen before it does, then test yourself with the quick check and the after-class practice set.