218. Graphics Effects from Equations Using Digital Tools

Learning Intentions

• Describe translations, stretches and reflections Use mathematical language.
• Match transformed graphs to corresponding equations.
• Justify parameter effects using graphical evidence.

Pre-requisite Summary

• Understand linear functions and quadratic functions .
• Recognise basic graph shapes (line, parabola).
• Understand gradient, intercepts, and vertex concepts.
• Identify horizontal and vertical shifts.
• Understand reflections in axes.
• Use digital graphing tools to visualise functions.

Worked Examples

Worked Example 1

Describe the transformation from:

to

Worked Example 2

Describe the transformation:

to

Worked Example 3

Match the graph to the equation:

Graph is a parabola opening downward with vertex at .

Possible equation:

Worked Example 4

Compare:

and

Worked Example 5

A graph shows:

• Same shape as
• Shifted left 2 units and up 1 unit

Write equation:

Problems

Problem 1

Describe the transformation:

Problem 2

Describe the transformation:

Problem 3

Match equation to transformation:

Describe shape and position changes.

Problem 4

Explain what happens when:

Problem 5

A parabola has vertex at and same shape as .

Write an equation.

Exercises

Understanding and Fluency

Exercise 1

Describe the transformation:

Exercise 2

Describe the transformation:

Exercise 3

Describe reflection:

Exercise 4

Describe stretch:

Exercise 5

Describe compression:

Exercise 6

State the vertex of:

Exercise 7

State the direction of shift:

Exercise 8

Identify transformation:

Exercise 9

Match description:

A parabola shifted up 4 units → write equation.

Exercise 10

Match description:

A parabola reflected and shifted down 2 units.

Reasoning

Exercise 11

Explain why changing does not affect the shape of a parabola.

Exercise 12

Explain how you know a graph is reflected from its equation.

Exercise 13

A student says:

“Changing moves the graph left 3 units.”

Explain the reasoning error.

Exercise 14

Justify how you can tell a graph is stretched vertically.

Problem-solving

Exercise 15

A model is:

Describe all transformations from .

Exercise 16

A graph shows:

• Vertex at
• Same shape as

Find equation.

Exercise 17

A parabola is reflected, stretched by factor 3, and shifted down 5.

Write an equation and explain each transformation.

Potential Misunderstandings

• Confusing left/right shifts in form.
• Thinking vertical stretch changes vertex position.
• Assuming reflections move the graph instead of flipping it.
• Believing changes shape of parabola.
• Mixing up translation direction in algebraic form.
• Forgetting that controls both stretch and reflection.
• Assuming vertex form is unrelated to transformations.
• Misreading combined transformations as separate unrelated changes.