Quadratic Equations
Telangana SSC Class 10 • Parabola • Roots • Discriminant
📘 Concept
A quadratic equation in one variable is of the form ax² + bx + c = 0, where a ≠ 0.
- The solutions (also called roots or zeros) are the x-values that satisfy ax² + bx + c = 0.
- The graph of y = ax² + bx + c is a parabola.
- If a > 0, the parabola opens upwards. If a < 0, it opens downwards.
Discriminant: Δ = b² - 4ac
- Δ > 0 → two distinct real roots
- Δ = 0 → one repeated real root
- Δ < 0 → no real roots (graph does not touch x-axis)
Axis of symmetry: x = -b / (2a)
Vertex (turning point):
x-coordinate of vertex = -b / (2a)
y-coordinate of vertex = value of y at that x.