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

Answer:Line one is the answer

Step-by-step explanation:

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