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2013 Term 1 Week 7 MATH PS GRAPHING CALCULATOR

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WHAT YOU WILL BE DOING IN THIS COURSE Graphic Calculator

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

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Familiarize yourself with the graphing calculators and its features

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Press 2 ND +712

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Press the MODE button

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Press WINDOW button Select Maximum and Minimum x- and y- values

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

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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 x1

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Type in the function in the parentheses, and divide the function by the restriction in the parentheses E.g. y=(x 2 5)/{x1} The and symbols are found by hitting 2 nd + MATH Function Domain

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McDonalds Sign

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4 Curves

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x y 4 02 What is the equation of this curve? 0 y = - (x+2) 2 + 8

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

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EquationDescription 1Y = -(X+2) 2 + 8 /{X0}Top left curve 2Y = -(X-2) 2 + 8 /{X0}Top right curve 3Y = -(2X+4) 2 + 4/{X0}Bottom left curve 4Y = -(2X-4) 2 +4/{X0}Bottom right curve

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2 nd + ZOOM (FORMAT)

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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

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

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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

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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

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Try it on your own

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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/(X0) and (X10)

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

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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?

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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)

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EquationDescription 1.0.25x 2 5 /{x-4 and x4}Bottom of the boat 2.-1/{x-4 and x4}Top of the boat 3.99x/{x>0.21and x0 and x5}Side of the mast 6.cos(2x+2)-5Waves 7.(0.9 2 -(x-7) 2 )+7.5Top of sun 8.-(0.9 2 -(x-7) 2 )+7.5Bottom of sun

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

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

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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

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More at the sabbatical website

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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

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

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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+ )+c y = a cos(bx+ )+c y = a tan(bx+ )+c a affects amplitude b affects period/frequency c affects y-intercept/height moves the graph horizontally Trigonometry