Graphing Quadratic Functions – A11

Graphs II – Edexcel GCSE (1MA1): Higher Tier

In this course, Professor Keith Ball (University of Warwick) continues exploring graphs, covering Topics A11-A13 in the Pearson Edexcel GCSE (9-1) Mathematics (1MA1) Specification for Higher Tier. In the first mini-lecture, we introduce quadratic functions, discuss how the various terms and their coefficients affect the shape of the corresponding graph, and take a look at turning points (Topic A11). In the second mini-lecture, we consider the roots, or solutions, of quadratic equations and look at graphs where there are two roots, one root, or zero roots (Topic A11). In the third mini-lecture, we explore turning points of quadratic functions, specifically how to determine the turning point by completing the square and how the sign of the x² term affects whether the turning point is a minimum or maximum (Topic A11). In the fourth mini-lecture, we consider the graphs of cubic functions and look at cubic graphs with three roots, two roots, or one root (Topic A12). In the fifth mini-lecture, we explore the graph of the reciprocal function (Topic A12) before turning towards exponential graphs in the sixth mini-lecture (Topic A12). In the seventh mini-lecture, we consider trigonometric graphs, including the graphs of sine, cosine, and tangent (Topic A12). In the eighth mini-lecture, we discuss translations and reflections of graphs (Topic A13).

Graphing Quadratic Functions – A11

In this mini-lecture we introduce Topic A11 by discussing quadratic functions, In particular, we focus on: (i) the key characteristic than all quadratic functions have: an x² term; (ii) a table of values satisfying y = x² and the corresponding graph; (ii) the parabola, which is the characteristic shape of all quadratic curves; (iii) the turning point and line of symmetry of y = x²; (iv) the graphs of y = x² – 2x and y =x² – 2x + 2 in comparison to y =x²; (v) quadratics with negative x² term and how this affects the turning point; (v) quadratics with coefficients in front of the x² term; and (vi) a table of values satisfying y = x² – x + 1 and the corresponding graph.