What you’ll learn5 learning objectivesChoose one objective for a focused lesson, or study the complete topic.1.1.1Completing the square• carry out the process of completing the square for a quadratic polynomial ax2 + bx + c and use a completed square form e.g. to locate the vertex of the graph of y = ax2 + bx + c or to sketch the graph.Syllabus objective1.1.2Quadratic discriminant• find the discriminant of a quadratic polynomial ax2 + bx + c and use the discriminant e.g. to determine the number of real roots of the equation ax2 + bx + c = 0. Knowledge of the term 'repeated root' is included.Syllabus objective1.1.3Quadratic equations• solve quadratic equations, and quadratic inequalities, in one unknown By factorising, completing the square and using the quadratic formula.Syllabus objective1.1.4Simultaneous equations• solve by substitution a pair of simultaneous equations of which one is linear and one is quadratic e.g. x + y + 1 = 0 and x2 + y2 = 25, 2x + 3y = 7 and 3x2 = 4 + 4xy.Syllabus objective1.1.5Quadratic-form equations• recognise and solve equations in x which are quadratic in some function of x. e.g. x4 - 5x2 + 4 = 0, xx61 0-+ =, tan2 x = 1 + tan x.Syllabus objective