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Review of Simple Sketching

Review of Simple Sketching. Last lesson we started reviewing the use of algebra for simple quadratic graph sketching. Ex1: Sketching y = x 2 + 2 x – 3 without using your graphic calculator. for TP let x = Sub into equation y = (-1) 2 + 2 -1 – 3 y = -4 So TP = (-1,-4).

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Review of Simple Sketching

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  1. Review of Simple Sketching Last lesson we started reviewing the use of algebra for simple quadratic graph sketching.

  2. Ex1: Sketching y = x2 + 2x – 3 without using your graphic calculator for TP let x = Sub into equation y = (-1)2 + 2-1 – 3 y = -4 So TP = (-1,-4) y = x2 + 2x – 3 for y int let x = 0 y = -3 so yint = (0,-3) for x int let y = 0 0 = x2 + 2x – 3 0 = (x + 3)(x – 1) x = -3, 1 xint = (-3,0) (1,0) Complete the square for TP y = x2 + 2x – 3 y = (x2 + 2x + 1) – 1 – 3 y = (x + 1)2 – 4 So TP = (-1,-4) An alternative to this method

  3. Ex2: Sketching y = (x + 2)2 – 9 without using your graphic calculator y = (x + 2)2 – 9 for y int let x = 0 y = (2)2 – 9 y = -5 so yint = (0,-5) for x int let y = 0 0 = (x + 2)2 – 9 0 = (x+2 + 3)(x+2 – 3) 0 = (x + 5)(x – 1) x = -5, 1 xint = (-5,0) (1,0) Find TP from equation TP = (-2,-9)

  4. Ex3: Sketching y = (x – 5)2 + 1 without using your graphic calculator y = (x – 5)2 + 1 for y int let x = 0 y = (-5)2 + 1 y = 26 so yint = (0,26) for x int let y = 0 0 = (x – 5)2 + 1 Can’t be factorised so no x intercepts Find TP from equation TP = (5,1)

  5. Ex4: Sketching y = 2x2 + x – 6 using your graphic calculator y = 2x2 + x – 6 for y int let x = 0 y = -6 so yint = (0,-6) for x int let y = 0 0 = 2x2 + x – 6 Using graphic calc. • Go to main menu • Enter expression (without y =) • Highlight • Interactive • Calculation • fmin Find TP using fmin on g calc

  6. Sketching using your graphic calculator Sketch the following using your graphic calculator Ex4E p111 Q4ade

  7. Ex5: Sketching y = 3x2 + 4x – 4 using your Graphs & Tables App • Go to Graphs & Tables • Analysis/Gsolve/min y = 3x2 + 4x – 4 for y int let x = 0 y = -4 so yint = (0,-4) for x int use root fn on g calc Find TP using min fn on g calc TP = (-0.666667, -5.33333) • Go to Graphs & Tables • Enter equation • Draw the graph using • Analysis/Gsolve/Root • Use left right direction button to move between the roots • If co-ordinates not showing up the click on Settings Menu (bottom) • Graph Format • Tick co-ordinates • Set

  8. Sketching graphs from the Graphs & Tables Application 6. y = 2x2 + 5x – 1 7. y = -2x2 + 8x – 6

  9. Ex7: Plottingy = x2 + 2x – 8 from graphs & tables application • On a piece of graph paper draw a set of axes with: • domain of x  [-6, 6] • range y  [-20, 100]

  10. Ex7: Plottingy = x2 + 2x – 8 from graphs & tables application • Go to Graph & Tables application • Clear the existing functions using Edit Clear All (or if you want to keep some functions for later make sure that they are unticked.) • Enter your function as y1 (or another y function) • Tick your function so that its graph will be drawn • Preview your graph by clicking the graph icon • Click on the table icon • Set the table starting and end points by clicking • Resize the screen to see the whole table • Plot the points • Clearly label all the significant points and if any are missing, work them out with you calculator. • Compare your graph to the one on your calculator

  11. PlottingPractice Questions Plot the following curves to your graph • y = x2 + 2x – 8 (previous example) • y = x2 + 4x – 12 • y = 2x2 + 5x – 7 • y = -3x2 + 2x + 8

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