Solutionbank C1 Edexcel Modular Mathematics for AS and A-Level Sketching curves Exercise E, Question 2 Question: (a) Sketch the curve y = f(x) where f(x) = (x − 1)(x + 2). (b) On separate diagrams sketch the graphs of (i) y = f(x + 2) (ii) y = f(x) + 2. (c) Find the equations of the curves y = f(x + 2) and y = f(x) + 2, in terms of x, and use these equations to find the coordinates of the points where your graphs in part (b) cross the y-axis. Solution: (a) f(x) = 0 ⇒ x = 1, − 2 (b)(i) f(x + 2) is a horizontal translation of − 2. (ii) f(x) + 2 is a vertical translation of + 2 Since axis of symmetry of f(x) is at x = − , the same axis of symmetry applies to f(x) + 2. Since one root is at x = 0, the other must be symmetric at x = − 1. (c) y = f(x + 2) is y = (x + 1)(x + 4). So x = 0 ⇒ y = 4 1 2 file://C:\Users\Buba\kaz\ouba\c1_4_e_2.html 3/10/2013 Heinemann Solutionbank: Core Maths 1 C1 Page 2 of 2 y = f(x) + 2 is y = x © Pearson Education Ltd 2008 2 + x = x(x + 1). So x = 0 ⇒ y = 0 file://C:\Users\Buba\kaz\ouba\c1_4_e_2.html 3/10/2013 Heinemann Solutionbank: Core Maths 1 C1 Page 1 of 2 Solutionbank C1 Edexcel Modular Mathematics for AS and A-Level Sketching curves Exercise E, Question 4 Question: (a) Sketch the graph of y = f(x) where f(x) = x(x − 2)2 (b) Sketch the curves with equations y = f(x) + 2 and y = f(x + 2). (c) Find the coordinates of the points where the graph of y = f(x + 2) crosses the axes. Solution: (a) y = x(x − 2)2 y = 0 ⇒ x = 0, 2 (twice) Turning point at (2 , 0) x → ∞ , y → ∞ x → − ∞ , y → − ∞ (b) (c) f(x + 2) = 0 at points where (x + 2) [ (x + 2) − 2 ] file://C:\Users\Buba\kaz\ouba\c1_4_e_4.html 3/10/2013 Heinemann Solutionbank: Core Maths 1 C1 Page 1 of 2 Solutionbank C1 Edexcel Modular Mathematics for AS and A-Level Sketching curves Exercise E, Question 5 Question: (a) Sketch the graph of y = f(x) where f(x) = x(x − 4). (b) Sketch the curves with equations y = f(x + 2) and y = f(x) + 4. (c) Find the equations of the curves in part (b) in terms of x and hence find the coordinates of the points where the curves cross the axes. Solution: (a) y = x(x − 4) is ∪ shaped and passes though (0 , 0) and (4 , 0). (b) f(x + 2) is a horizontal translation of − 2. f(x) + 4 is a vertical translation of + 4.
