2 Quadratic Functions
C H A P T ER
Topics
Key words
2.1 The quadratic function
intercept, maximum point, minimum point, quadratic function, root, turning point
2.2 Completing the square
coefficient, completing the square,
2.3 Domain and range
range
2.4 The discriminant
discriminant, real roots, soluble, square root
2.5 Intersecting graphs
chord, Intersection, tangent
2.6 Solving quadratic equations
difference of two squares, factors, quadratic equations, quadratic formula, surds
2.7 Quadratic inequalities
number line, quadratic inequality, range
In this chapter you will learn how to • Solve and manipulate quadratic functions and equations and how these relate to quadratic graphs and their maximum and minimum points. • Find the maximum or minimum value of the quadratic function f : x → ax2 + bx + c by sketching • Find the maximum or minimum value of the quadratic function f : x → ax2 + bx + c by completing the square • Use the maximum or minimum value of f(x), xx), where one of a, b or c is unknown to find work out f(x) xx) and sketch the graph or determine the range for a given domain. • Know the conditions for f(x) x = 0 to have (i) two different real roots, (ii) two equal roots, x) (iii) no real roots • Know how the number of real roots relate to a given line (i) intersecting a given quadratic curve twice, (ii) being a tangent to a quadratic curve, (iii) not intersecting a quadratic curve • Solve quadratic equations for real roots using (i) factorisation, (ii) the quadratic formula, (iii) completing the square • Solve a quadratic inequality and determine the domain for which certain inequalities are valid.
From your IGCSE Mathematics course you should be able to •
recognise, sketch and interpret graphs of quadratic functions
•
identify and interpret roots, intercepts and turning points of quadratic functions graphically
•
know the symmetrical property of a quadratic.