2024 JPJC Chapter 2 Graphing Techniques I

Chapter 2 Graphing Techniques I (Students’ version) / Pg 1 Jurong Pioneer Junior College H2 Mathematics (9758) JC1-2023 References  http://www.h2maths.site [This website offers Applets which allow self-exploration of numerous types of graphs covered in this topic]  H2 Mathematics For 'A' Level, Federick Ho, David Khor, Yui-P'ng Lam, B.S. Ong Volume 1, Call No 510.76 HO  Mathematics The Core Course for A-level, L Bostock and Chandler, Call No 510 BOS  MEI Structured Mathematics (2 nd Edition), Pure Mathematics 4, Terry Heard and David Martin, Call No 510 HEA  Pure Mathematics 4, Hugh Neill and Douglas Quadling, Call No 510 NEI Prerequisites  Long division of polynomials (O level Add Math knowledge)  Graphs (including trigonometry)(O level Elementary and Add Math knowledge)  Quadratic graphs and their properties (O level Add Math knowledge)  Differentiation techniques and applications (O level Add Math knowledge)  Coordinate geometry and Further Coordinate Geometry (O level Add Math knowledge) Content requirement Include: • use of a graphic calculator to graph a given function • important characteristics of graphs such as symmetry, intersections with the axes, turning points and asymptotes of the following: 2 2 2 2 1x y a b  2 2 2 2 2 2 2 2 1; 1x y y x a b a b    ax by cx d   2ax bx cy dx e    • determining the equations of asymptotes, axes of symmetry, and restrictions on the possible values of x and/or y • simple parametric equations and their graphs Chapter 2: Graphing Techniques I

Chapter 2 Graphing Techniques I (Students’ version) / Pg 2 Jurong Pioneer Junior College H2 Mathematics (9758) JC1-2023 1 Basic Graphs 1.1 Straight Lines A straight line that is not a vertical line has an equation in the form y = mx + c, where m is the gradient of the line and c is the y-intercept. The equation in this form is called the gradient-intercept form. Lines that are not vertical Vertical line x y O c x y O c x y O c x y Ok 1.2 Quadratic Functions y = ax2 + bx + c, a  0 A quadratic function has an equation in the form 2y ax bx c   where 0a  . The graph of a quadratic function is a parabola and its concavity is determined by a. The graph has a turning point at 2 bx a  . Concavity of graph a > 0 Concave upwards xO y x = 2a b c xO x = 2a b c y xO y x = 2a b c a < 0 Concave downwards xO y x = 2a b c xO x = 2a b c y xO y x = 2a b c Note: If the equation of a quadratic graph is expressed in the form   2 y a x h k   , then the coordinates of the turning point are  ,h k .

Chapter 2 Graphing Techniques I (Students’ version) / Pg 3 Jurong Pioneer Junior College H2 Mathematics (9758) JC1-2023 Recall: Find the turning point of 22 5 3y x x   Solution: Method 1: 2 2 2 2 2 2 2 2 5 3 52 3 2 5 5 52 3 2