2013 Term 1 Week 7 MATH PS GRAPHING CALCULATOR

WHAT YOU WILL BE DOING IN THIS COURSE… Graphic Calculator

OUTLINE OF COURSE Basic Skills - Reset - Windows - Mode - Format Functions - Lines - Quadratic - Trigo. Design

 Familiarize yourself with the graphing calculators and its features

 Press “2 ND” “+”712

 Press the ‘MODE’ button

 Press ‘WINDOW’ button  Select Maximum and Minimum x- and y- values

 Press the ‘Y=’ button  Write functions to create pictures  Use your mathematical knowledge  You can use up to 10 equations on the ‘Y=’ screen

 Sometimes you may only require to graph a portion of the domain  E.g. The function is y=x 2 – 5 but it is only graphed for x≥1

 Type in the function in the parentheses, and divide the function by the restriction in the parentheses  E.g. y=(x 2 – 5)/{x≥1}  The ≥ and ≤ symbols are found by hitting ‘2 nd ’ + ‘MATH’ Function Domain

 McDonald’s Sign

 4 Curves

x y 4 0−2 What is the equation of this curve? 0 y = - (x+2) 2 + 8

 Find the equations & domains of ALL 4 curves and draw your McDonald’s sign  To help you, here are the WINDOW setting:

EquationDescription 1Y = -(X+2) /{X≤0}Top left curve 2Y = -(X-2) /{X≥0}Top right curve 3Y = -(2X+4) 2 + 4/{X≤0}Bottom left curve 4Y = -(2X-4) 2 +4/{X≥0}Bottom right curve

 ‘2 nd ’ + ‘ZOOM’ (‘FORMAT’)

 ‘2 nd ’ + ‘PRGM’ (‘DRAW’)  7: Shade(Y 3,Y 1 )  Y 1 : bottom Y equation, Y 3 : top Y equation  Press ‘VARS’, move to ‘Y-VARS’ menu  Press 1: Function  Choose the equation

 ‘2 nd ’ + ‘PGRM’ (‘Draw’)  0: TEXT  (ALPHA followed by letters)

 ‘2 nd ’ + ‘PGRM’ (‘DRAW’)  Use the arrow key to move to ‘STO’ menu  1: StorePic  Key in a number from 1 to 9  Press Enter

 ‘2 nd ’ + ‘PRGM’ (‘DRAW’)  Use the arrow key to move to ‘STO’ menu  2: RecallPic  Key in the number where you store it  Press Enter

 Try it on your own…

 To restrict domain on both sides Use the ‘and’ function ‘2 nd ’ + ‘MATH’ (‘TEST’)  Use your arrow key to move to ‘LOGIC’ menu 1: and E.g. -(X + 2) 2 + 8/(X≥0) and (X≤10)

 To draw the Sun  Equation of the circle: X 2 + Y 2 = r 2

 Vertical lines cannot be graphed in function mode  However, a very steep line can be produced  What is y=x?  Now, what is y=50x?  …

 Try it on your own… Set 2 domains Either use circle formula (make y the subject) or use 2 quadratic curves Trigo Function Use a large gradient (i.e. m>94) Use a large gradient (i.e. m>94)

EquationDescription x 2 – 5 /{x≥-4 and x≤4}Bottom of the boat 2.-1/{x≥-4 and x≤4}Top of the boat 3.99x/{x>0.21and x<0.24}Pole 4.0/{x≥0 and x≤5}Bottom of the mast 5.-2x+10 /{x>0 and x≤5}Side of the mast 6.cos(2x+2)-5Waves 7.√( (x-7) 2 )+7.5Top of sun 8.-√( (x-7) 2 )+7.5Bottom of sun

Or “How to draw a batman logo or a butterfly with a single equation in GC?”

 To set your graphic calculator to Polar Coordinates…  Mode > POL > [Enter]

 You have now changed Cartesian coordinates to Polar coordinates.  Press and you will see that y is no longer the subject but r.  Explore the following curves using the GC…

More at the sabbatical website…

y=mx+c m=gradient, c=y-intercept vertical lines: use horizontal lines with very steep gradients (y=ax, a>94) Lines y=ax 2 +bx+c a determines how open the parabola should be and in which direction b affects turning point c affects y-intercept y=a(x-h)2+k derive from completing the square h & k are x & y coordinates of vertex point Quadratic

y=px 3 +qx 2 +rx+c Cubic (x-a) 2 +(y-b) 2 =r 2 r = circle radius the centre’s coordinates are (a,b) please make y the subject of this formula first hint: you will get 2 formulas Circle

x 2 /a 2 + y 2 /b 2 = 1 if a>b majors along x-axis a = x-intercept, b = y-intercept if b>a majors along y-axis a = y-intercept, b = x-intercept Ellipse y = a sin(bx+ θ )+c y = a cos(bx+ θ )+c y = a tan(bx+ θ )+c a affects amplitude b affects period/frequency c affects y-intercept/height θ moves the graph horizontally Trigonometry