Using the CASIO fx-82ZA PLUS for functions in the FET band

1. Using the CASIO fx-82ZA PLUS for functions in the FET band Rencia Lourens RADMASTE Centre

2. Some remarks • A calculator is a tool. • Learners should • Know where answers come from. • Understand mathematics. • Teachers should • Teach the mathematics. • Explain the reasoning behind why the calculator methods work. • BUT the calculator can (and should) become a tool to assist.

3. CAPS • Functions form 35% of the Grade 12 paper 1, 45% in Grade 11 and 30% in Grade 10 (CAPS). The calculator can be used to support the calculations needed to draw and interpret the graphs of the functions.

4. Intersection of two graphs • Find the points of intersection of the straight line f(x) = x – 3 and the parabola g(x) = x2 – x – 6 if . • We need to be • Be in TABLE mode. • Have the DUAL table SETUP. Who is NOT sure?

5. So how can I as a teacher use this to enhance understanding? • Some thoughts • The meaning of simultaneous equations. • The meaning of a plotted graph.

6. Next example • Find the point(s) of intersections of the graphs and • This example is different from the previous one because • The domain is not given • It is not a convenient example where the answer(s) are “in your face”. • So we choose our own domain and start with

7. f(-2) > g(-2) f(-1) < g(-1) f(3) < g(3) f(4) > g(4)

8. Hence somewhere between x = -2 and x = -1 we will have f(x) = g(x). (We will look at the other value later on). • We keep the table as is, but change our domain to • We also change the steps and make that 0,25.

10. Also somewhere between x = 3 and x = 4 we will have f(x) = g(x). • We keep the table as is, but change our domain to • We also change the steps and make that 0,25.

12. The graphs and intersect at • (-1,5; 2,75) • (3,5; 2,25)

13. Turning point of a parabola • Find the turning point of • We do not know the range so we will start with • We do not need the second function, so we CAN disable the second function.

15. So how can I use this as a teacher to enhance understanding? • Some thoughts • The meaning of symmetry • The minimum value • The meaning of a plotted graph • The shape of a quadratic function • Just checking – the turning point is (2; -5)

16. New example • Find the turning point of • We do not have a domain so we start with .

17. The turning point should be somewhere between x = 0 and x = 1

18. So…….. • We keep the table and change the domain to…. • And we make the steps…..

19. The turning point is

20. Next example • Find the turning point of . • We do not know the domain hence…

21. The turning point should be somewhere between x = 1 and x = 3

22. We will change the domain to . • The steps should be .

23. The turning point should be somewhere between x = 2 and x = 2.25

24. We will change the domain to . • The steps should be .

25. The turning point is

26. Finding the intercepts with the axes • Find the intercepts with both the axes of the graph of . • Domain . • Steps of 1

27. Just checking……. Where will the turning point be? y intercept x intercept x intercept

28. So how can I as a teacher use this to enhance understanding? • Some thoughts • The meaning of vs the meaning of . • The meaning of a plotted graph • Solving of quadratic equation

29. Next example • Find the intercepts with both the axes of . • Domain . • Steps of 1.

30. y-intercept Turning point should be here No x-intercept?

31. Seems as there are no x-intercepts. • Focus on turning point first. • Will be between x=1 and x=2. • The turning point is below the x-axis. • All the graph values are below the x-axis. • So no x-intercepts.

32. Next example • Find the intercepts with both the axes of . • Domain . • Steps of 1.

33. y-intercept Turning point should be here x-intercept should be here x-intercept should be here

34. Somewhere between x = -2 and x = -1 the one x-intercept should lie and somewhere between x = 3 and x = 4 the other x-intercept should lie. • So we are going to look at smaller domains and smaller steps.

35. x-intercept

36. x-intercept

37. Looking at the reciprocal function • Work with domain

38. y-intercept Asymptote x-intercept

39. Finding equations of graphs • We now need to move to the STATS mode • Let us have a look at the Menu • Is everybody sure how to get into STATS mode?

40. Example – linear function • We are going to work with the linear regression. • Find the equation of the straight line through (-1; -1) and (2; 5). • Type in the two points in the table (data). • Find the coefficients remembering that in stats the linear equation is . • The equation is . • Or as we know it .

41. Example – Quadratic function with intercepts given • Typing error on page 10 (first bullet please change to Quadratic and not linear). • Enter the three points in the table (data). • Find the coefficients remembering that in stats the linear equation is . • The equation is . • Or as we know it .

42. Example – Quadratic function with any three points. • Enter the three points in the table (data). • Find the coefficients remembering that in stats the linear equation is . • The equation is . • Or as we know it .

43. Example – Exponential function* with any two points. • Enter the two points in the table (data). • Find the coefficients remembering that in stats the linear equation is . • The equation is . • *The CASIO fx-82ZA PLUS calculator can only do the exponential graph of the form .

44. Example – Quadratic function with the turning point and another point. • We need to find ANOTHER point. • From the turning point we know the axis of symmetry is at x = -1 • The point symmetrical to (0;5) will be (-2; 5). • Enter the three points. • Find the coefficients remembering that in stats the linear equation is . • The equation is . • Or as we know it .