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Parabola Explorer

Four letters, one curve — turn them one at a time and see which does what.

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f(x) = a(b(x − c))² + d

f(x) = x²

−8−8−6−6−4−4−2−2224466880

f(x) = x²

Vertex (0, 0) · opens upward · crosses the y-axis at 0

It touches the x-axis once, at x = 0.

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The four letters

asteeper / flips1
bnarrower / wider1
cleft and right0
dup and down0

Turning one letter sends the other three back to 1, 1, 0, 0 — so whatever changes on screen was that letter and nothing else.

Sweep a letter

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Using it in class

  1. Leave “one at a time” on and sweep a, then b, then c, then d. Ask what moved before saying.
  2. Stop anywhere and ask where the vertex is — it is always (c, d), whatever a and b are doing.
  3. Turn b negative and ask why nothing happened. That is the lesson that b is squared.
  4. Switch on the expanded form and ask which of a, b, c, d changed the x² coefficient.