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 question is asking which numbers are larger with respect to one another. An easy way to do this is to convert to decimals, or just memorize it. 1/2=0.5, 3/4=0.75, 2/3=0.666666. So descending order (largest to smallest) 3/4, 2/3, 1/2.
