Cambridge O Level Additional Mathematics · Syllabus 4037 · Quadratic Functions
Range of a Quadratic Function
What is Range of a Quadratic Function?
The set of output values a quadratic function actually takes over its stated domain. For an upward parabola with turning point (h, k) and no domain restriction the range is f(x) greater than or equal to k; for a downward parabola it is f(x) less than or equal to k. When the domain is restricted the range must be read from the part of the curve that survives: if the turning point lies inside the domain it still supplies one boundary, but if it lies outside, the function is monotonic there and every boundary the range has comes from an endpoint of the domain instead. A closed interval supplies two endpoints and so gives a range bounded on both sides, while a one-sided domain such as x greater than or equal to 3 supplies one endpoint and gives a range bounded on one side only.
This definition is part of the Quadratic Functions chapter in Cambridge O Level Additional Mathematics.