Two sets of quadratic expressions are shown below in various forms: line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25 line 2: x2 + 5x + 6 (x + 2)(x + 3) (x + 2.5)2 + 6.25 which line contains three equivalent expressions? line 1 only line 2 only both line 1 and line 2 neither line 1 nor line 2

Line 1:
Expanding the vertex form, we have
  x² + 2·1.5x + 1.5² - 0.25 = x² +3x +2
Expanding the factored form, we have
  x² +(1+2)x +1·2 = x² +3x +2
Comparing these to x² +3x +2, we find ...
  • the three expressions are equivalent on Line 1

Line 2:
Expanding the vertex form, we have
  x² +2·2.5x +2.5² +6.25 = x² +5x +12.5
Expanding the factored form, we have
  x² +(2+3)x +2·3 = x² +5x +6
Comparing these to x² +5x +6, we find ...
  • the three expressions are NOT equivalent on Line 2

The appropriate choice is
  Line 1 only

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