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C1: Chapters 1-4 Revision Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 10 th October 2013

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Solving simultaneous equations Remember that the strategy is to substitute the linear equation into the quadratic one, then solve. ?

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Expanding out correctly! ?

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Find the set of values of x for which (a) 4x – 3 > 7 – x (b) 2x 2 – 5x – 12 7 – x and 2x 2 – 5x – 12 < 0 Inequalities ? ? ?

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Discriminant ? ? ?

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Sketching quadratics/cubics

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Sketching cubics Sketch the following, ensuring you indicate the values where the line intercepts the axes. y = (x+2)(x-1)(x-3) y = x(x-1)(2-x) y = x(2x – 1)(x + 3) y = x 2 (x + 1) y = x(x+1) 2 y = x(1 – x) 2 y = -x 3 y = (x+2) 3 y = (3-x) 3 1 2 3 4 5 6 7 8 9 10 11 12 y = (x+2) 2 (x-1) y = (2-x)(x+3) 2 y = (1 – x) 2 (3 – x) -2 13 6 1 2 0.5 3 1 -2 8 1 3 -3 18 -2 1 3 27 -4 2 3 ? ? ? ? ? ? ? ? ? ? ? ?

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Transforming Existing Graphs a f(bx + c) + d Bro Tip: To get the order of transformations correct inside the f(..), think what you’d need to do to get from (bx + c) back to x. Step 1: c Step 2: ↔ b Step 3: ↕ a Step 4: ↑ d ? ? ? ?

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Transforming Existing Graphs Here is the graph y = f(x). Draw the following graphs, ensuring you indicate where the graph crosses the coordinate axis, minimum/maximum points, and the equations of any asymptotes. (2, 3) 1 x y y = -1 y = f(x) 6 x y y = -2 y = 2f(x+2) y = f(2x) 1 x y y = -1 (1, 3) y = -f(-x) – 1 -2 x y y = 0 (-2, -4) ? ? ?

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Sketching Graphs by Considering the Transform ? ?

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x y -2 -0.5 ? Sketching Graphs by Considering the Transform

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x y ?

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Sketching Quadratics Sketch y = x 2 + 2x + 1Sketch y = x 2 + x – 2 x y x y 1 1 -21 Sketch y = -x 2 + 2x + 3 x y 3 3 Sketch y = 2x 2 – 5x – 3 x y -3 -0.53 ?? ??

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Sketching Quadratics Sketch y = x 2 – 4x + 5 x y (2, 1) 5 Sketch y = -x 2 + 2x – 3 y -3 (1,-2) ? ? ? ? ?

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