The Math Meridian
Back to Quadratic Functions

Where a line meets a parabola

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Useful for: MCR3U IB Math AA SL & HL

Learn it Set the two equations equal and rearrange into ax² + bx + c = 0. The discriminant says how many times they meet: 2 (secant), 1 (tangent) or 0. Solve to find the x-coordinates, then substitute for y.

Example: How many times does y = 2x + 1 meet y = x² + 3?

  1. x² + 3 = 2x + 1 → x² − 2x + 2 = 0.
  2. D = 4 − 8 = −4 < 0: they don't meet.

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