Question

Two sets of quadratic expressions are shown below in various forms:

Line 1: x2 − x − 6 (x + 2)(x − 3) (x + 0.5)2 − 6.25
Line 2: x2 − x − 2 (x + 1)(x − 2) (x − 0.5)2 − 2.25

Which line contains three equivalent expressions?


The correct answer is line 2 only
(I am doing this because I couldn't figure out how to answer the actual question because it had a pre existing answer so I could figure it out) So my real question is how to answer questions that are already answered

Answer 1

To prove that the answer is line 2, you would need to disprove that the answer is line 1.
To disprove line 1, we can expand both expressions in the brackets and see if they are equivalent to x² - x - 6

(x + 2)(x - 3) = x² + 2x - 3x - 6 = x² - x - 6
So those brackets are equivalent

(x + 0.5)²
= (x + 0.5)(x + 0.5) = x² + 0.5x + 0.5x + 0.25 = x² + x + 0.25
x² + x + 0.25 - 6.25 = x² + x - 6

So line 1 is incorrect because (x + 0.5)² - 6.25 is not equivalent to x² - x - 6.

I hope this helps! Let me know if you would like me to show you how to prove that line 2 is correct :)