Curriculum
Pure Mathematics — Second Secondary
Unit 1: Real Functions and Curve Sketching
0/8
Unit 2: Exponents and Logarithms
0/12
Unit 3: Limits
0/6
Unit 4: Trigonometry
0/4
Text lesson
Monotonicity of Functions
Monotonicity of Functions
Monotonicity of a quadratic function
Monotonicity of a quadratic function
- The graph of f(x) = ax² + bx + c is a parabola.
- Its vertex is the turning point that separates the two intervals of monotonicity.
- The x-coordinate of the vertex is x0 = −b / (2a).
Key points
If a > 0 (the parabola opens upward)f is decreasing on ]−∞, x0] and increasing on [x0, ∞[.
If a < 0 (the parabola opens downward)f is increasing on ]−∞, x0] and decreasing on [x0, ∞[.
Monotonicity of Functions · 3 / 6