Range of a Quadratic Function (Vertex Formula)
For a quadratic function f(x) = ax² + bx + c \ (a eq 0), its range depends on the opening direction and the y - coordinate of the vertex. Vertex x - coordinate…
Syllabus path: Functions › Concepts and Properties of Functions › Range of a Function
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CSCA Mathematics Formula Reference
Formula and explanation
For a quadratic function f(x) = ax² + bx + c \ (a eq 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 onto t…
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