216. Quadratic Parameters
Learning Intentions
- Identify parameters in quadratic functions.
- Describe how parameter changes affect the shape and position of a parabola.
- Compare algebraic changes with graphical transformations.
Pre-requisite Summary
- Understand quadratic functions in the form
. - Recognise the role of coefficients in shaping graphs.
- Plot basic parabolas using tables of values.
- Identify intercepts and turning points.
- Understand graph transformations (shifts and stretches).
- Substitute values into quadratic expressions.
Worked Examples
Worked Example 1
Identify the parameters in:
State the values of:
Worked Example 2
Compare:
and
Worked Example 3
Compare:
and
Worked Example 4
Compare:
and
Worked Example 5
Compare algebraic and graphical change:
Problems
Problem 1
Identify
Problem 2
Describe the effect of:
Problem 3
Describe the transformation:
Problem 4
Describe the transformation:
Problem 5
Explain the effect of:
Exercises
Understanding and Fluency
Exercise 1
Identify parameters
Exercise 2
Identify parameters:
Exercise 3
Identify parameters:
Exercise 4
Describe effect of changing
Exercise 5
Describe effect of changing
Exercise 6
Describe effect of:
Exercise 7
Describe shift:
Exercise 8
Describe shift:
Exercise 9
State what changes when
Exercise 10
State what remains unchanged when only
Exercise 11
Explain why
Exercise 12
Explain why
Exercise 13
A student says:
“Changing
only moves the graph up or down.”
Explain the error.
Exercise 14
Explain the difference between:
Exercise 15
Interpret:
Exercise 16
Compare:
A:
B:
Exercise 17
Describe the full transformation:
Potential Misunderstandings
- Thinking
only shifts the graph (it affects vertex position). - Confusing
with the turning point. - Assuming all changes affect shape (only
affects shape). - Misunderstanding
as shifting left instead of right. - Forgetting negative
reflects the graph. - Mixing expansion form
with vertex form. - Assuming symmetry changes when
changes.
Next: 217. Exploring Linear and Quadratic Relations with Digital Tools