Year 9 Interactive Maths - Second Edition

Projects

Project 10.1  Transformations of Quadratic Functions

Investigate how a and c affect the graph of y = x² in the equation of y = ax² + c.

Note:

If you have a TI-83 Graphing Calculator, clear all the Y= entries before graphing each new set of quadratic functions in the project's questions.  The calculator will display the graphs in order.  The graph of Y₁ will be displayed first, followed by Y₂, etc.  Set Y_1, Y₂ and Y₃ to graph a dotted, solid and thick line respectively.

Suggested dimensions of the viewing window for this project are [-10, 10], Xscl = 1 and Yscl = 1, i.e. use ZOOM 6.

1a.  Graph the following functions on the same set of axes:

  b.  What do the graphs have in common?

  c.

  d.

2a.  Graph the following functions on the same set of axes:

  b.  What do the graphs have in common?

  c.

  d.

3a.  Graph the following functions on the same set of axes:

  b.

  c.

4a.  Graph the following functions on the same set of axes:

  b.

  c.

5a.  Graph the following functions on the same set of axes:

  b.

  c.

  d.

  e.

  f.

Project 10.2  Minimum Value

2.  Complete the following table using a graphics calculator or otherwise:

3.  Plot the graph of N against x.

4.  State the minimum value of N and the value of x for which it occurs.

Project 10.3  Vertical Translation

3.  What do the graphs have in common?

4.  What are the coordinates of the y-intercepts and turning points in terms of c?

Project 10.4  Dilation

3.  What does the family of parabolas have in common?

4.  What do the turning points have in common?

Project 10.5  Vertical Translation

3.  What does the family of parabolas have in common?

4.  What do the turning points have in common?

Project 10.6  Transformations of Quadratic Functions

Investigate how b affects the graph of y = x² in the equation of y = (x - b)².

Note:

If you have a TI-83 Graphing Calculator, clear all the Y= entries before graphing each new set of quadratic functions in the project's questions.  The calculator will display the graphs in order.  The graph of Y₁ will be displayed first, followed by Y₂, etc.  Set Y_1, Y₂ and Y₃ to graph a dotted, solid and thick line respectively.

Suggested dimensions of the viewing window for this project are [-10, 10], Xscl = 1 and Yscl = 1, i.e. use ZOOM 6.

1.   Graph the following quadratic functions on the same set of axes:

2.

How are the graphs alike?

6.

7.

8.

9.

10.

11.