• To recognise a quadratic function: y = f (x) = ax 2 + bx + c. • To be able to plot a graph of a quadratic function.
• To be able to fi nd properties of quadratic functions (crossing axes, vertices, axis of symmetry).
• To work with intersecting quadratic functions. • To use quadratic functions to solve real-life problems.
17.1 What is a quadratic function?
A quadratic function is a relationship between two variables x and y that can be written in the form y = f (x) = ax 2 + bx + c, where a, b, c are constant real numbers, a ≠ 0.
a is called the coeffi cient of x 2. b is called the coeffi cient of x. c is called the constant term.
They have many applications in areas such as architecture (arches), economics, engineering, mechanics and physics.
The trajectory (path) of a javelin is described by a quadratic function, as shown:
