Range of a Quadratic Function (Vertex Formula)
For a quadratic function f(x) = ax² + bx + c \ (a ≠ 0), its range depends on the opening direction and the y-coordinate of the vertex.
Syllabus path: Functions › Concepts and Properties of Functions › Range of a Function
CSCA Exam Prep
This formula is aligned to the CSCA undergraduate admissions exam syllabus. Continue with the linked tutorial and topic practice.
Practice related questions (13) · Start mock exam · Sign up — AI explanations · Membership plans
CSCA Mathematics Formula Reference
Formula and explanation
For a quadratic function f(x) = ax² + bx + c \ (a ≠ 0), its range depends on the opening direction and the y-coordinate of the vertex. Vertex x-coordinate: x₀ = -(b)/(2a). Vertex y-coordinate (extreme value): y₀ = f(x₀) = (4ac - b²)/(4a). Range: - If a > 0, range is [y₀, + ∞). - If a < 0, range is (-∞, y₀]. Condition: Domain is all real numbers ℝ.
Related tutorial and examples
Range of a Function
Range of a Function 1. Concept The range of a function y = f(x) is the set of all possible output values y corresponding to the input values x in the domain D. It is denoted as R_f = { f(x) | x ∈ D }. Intuitive Understanding: If you project the graph of a function horizontally on…
Plan your next CSCA study step
Use this topic in a focused practice set, then connect it to the exam requirements and timed papers.