Av1 matematica

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Exploring the vertical shift of a parabola
Stephen Sproule
St John’s College, Johannesburg, South Africa
Introduction
Advancements in scientific calculators are substantially contributing to the teaching of mathematics in developing nations. Computers and even graphics calculators are cost prohibitive for the vast majority of students in many developing countries. However with progress in scientific calculators, such as the
Casio ES series (Casio FX-82ES ; Casio FX-82ES – PLUS ; Casio FX-991ES ; Casio FX-991ES –
PLUS), mathematics teachers are able to use this technology as a teaching tool not just a calculating device. Teacher’s notes
This lesson is an investigation of the vertical shift of the parabolic function, f ( x )  q  x 2 .
It is part of a set of investigations, exploring the horizontal and vertical shifts of the parabola, rectangular hyperbola and exponential function.
Pre-knowledge:

Students must have drawn a few graphs of the parabola in the form, f ( x )  x 2 .
Students do not need to be able to use the properties of the parabola to draw the graph. This activity will use the table method to draw the graph.

Calculator’s role:

Requiring students to repeatedly complete the table for a function can be cumbersome and requiring it for a number of shifts of a function would waste valuable teaching time. The calculator helps make the activity time efficient and limits computation errors, ensuring greater access to the actual exploration.

Mathematics:

In this activity we use the notation ( y  q )  x 2 instead of f ( x )  x 2  q . This ensures that students associate the shifts with ( y  q ) and ( x  p) . The teacher can then later introduce f ( x )  x 2  q as common practice.

Equipment:

10cm × 10cm piece of tracing (patty) paper

Grade: 10 or 11

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Lesson
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The worksheets given below come in a set of four. Each worksheet looks remarkably