Special Cases in Systems of Equations

learning_notes

Last updated: 8/16/2025

Key Concepts:

  • One Intersection: When a quadratic and linear equation meet at exactly one point.
  • No Intersection: When equations have no common solution.
  • Multiple Intersections: When equations meet at more than one point.

Skills Covered:

  • Recognizing how different graphs intersect
  • Determining special cases of systems

Example Problems:

  • Find the value of k such that the line (y = kx + 3) is tangent to the parabola (y = x^2 - 4x + 3).
  • Explain why the system (y = x^2 + 4) and (y = -x^2 + 1) has no solutions.

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