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At how many points does the graph of cut the -axis?

Class 10Quadratic EquationsAlgebra — Quadratics
  • ATwo points
  • BOne point
  • CIt never cuts the -axis
  • DThree points

Step-by-Step Solution

The graph meets the -axis where , so there are two distinct real roots and the curve crosses twice (at and ). One point would need ; never cutting would need — but subtracting a negative c makes larger, not smaller. A quadratic graph can never meet the axis three times, since a degree-2 equation has at most two roots.
Answer: A) Two points

Key idea: The discriminant — nature of roots

classifies the roots of **: TWO distinct real roots. Parabola crosses -axis at two points.
- ****: ONE repeated real root (called a 'double root' or 'two equal roots'). Parabola touches -axis at the vertex.
- ****: NO real roots. Parabola does not touch the -axis at all.

**Use case**: 'For what values of does have equal roots?' → set → .

You can answer 'how many real roots?' WITHOUT computing them — just compute .

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