The Math Meridian
Back to Quadratic Relations

Find the equation of a parabola

Questions at easy, medium and hard levels. Pick a level and get a fresh set every time, with instant feedback.

Learn it Pick the form that matches what you know. Vertex (h, k) known: y = a(x − h)² + k. Zeros r and s known: y = a(x − r)(x − s). Then substitute one more point to find a.

Example: A parabola has vertex (2, −3) and passes through (4, 5). Find a.

  1. y = a(x − 2)² − 3.
  2. 5 = a(4 − 2)² − 3 → 5 = 4a − 3 → 4a = 8.
  3. a = 2, so y = 2(x − 2)² − 3.

Loading questions…