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Common Mistakes

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Frequent Errors

1. Using y - k = a(x - h)^2 when parabola opens left/right (4.6.A.1). 2. Misreading vertex as center on parabola problems (4.6.A.1). 3. Treating ellipse denominators a^2, b^2 as radii without sqrt when graphing (4.6.A.2). 4. Forgetting circle is a = b special case (4.6.A.2). 5. Ellipse form with minus sign (hyperbola confusion) (4.6.A.3). 6. Hyperbola opening direction from wrong squared term (4.6.A.3). 7. Omitting asymptotes on hyperbola sketches (4.6.A.3). 8. Classifying any two-term equation without checking structure (2.A).

Why These Happen

Students memorize one template and force all equations into it.

How to Fix Them

  • Count squared terms and check plus vs minus.
  • Match parabola form to opening direction.
  • Label h, k, a, b before plotting.

Avoidance Scripts

  • "One square: parabola. Plus both: ellipse. Minus: hyperbola."
  • "Vertex for parabola; center for ellipse/hyperbola."
  • "Circle means a = b."

Quick Self-Check

  • Did I identify the conic type first?
  • Is (h, k) read from the correct form?
  • For hyperbola, did I note asymptotes?

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