6.12.7  Canonical form: canonical_form

The canonical form of a second degree polyomial in a variable x is the form a(x−c)²+b.

The canonical_form command finds the canonical form of a second degree polynomial.

• canonical_form takes one argument:
  p, a second degree polynomial.
• canonical_form(p) returns the canonical form of p.

Examples.

• Input:
  canonical_form(x^2-6*x+1)
  Output:

  ⎛ ⎝

  x−3

  ⎞ ⎠

  2−8

• Input:
  canonical_form(2*t^2+3*t+8)
  Output:

  2

  ⎛ ⎜ ⎜ ⎝

  t+

  3 4

  ⎞ ⎟ ⎟ ⎠

  2

  +

  55 8