Query about Question 2 from "PrepSwift: Finding the Minimum Value" [3207] _ I didn't understand the official solution

[user8618]

https://prepswift.gregmat.com/quizzes/quiz/prepswift-finding-the-minimum-value (Question 2)

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In this question, I multiplied both sides by -ve sign, to ensure that the RHS is in a more familiar quadratic equation state, with x^2 being positive.

I then used completing the square method and the final equation came out to be y= - (x+0.5)^2 + 1.25.

Looking at this equation, I thought the answer is D. (x+0.5)^2 will always be non-negative. But due to a negative sign outside the brackets, it will always be negative.

Which means that if x=0, then y = 1. But if x>1, then y < 1.

Can you please explain what I did wrong?

[cylverixxx]

@user8618

Looking at this equation, I thought the answer is D. (x+0.5)^2 will always be non-negative. But due to a negative sign outside the brackets, it will always be negative.

It’s asking about the minimum value, or rather, it’s asking about one particular value. It can’t possibly be D because you’re comparing two real numbers, so a “relationship” can definitely be determined.

[user8618]

Apologies but I still don’t understand the solution.

Would it be possible for you to breakdown the solution in a simpler manner please?

[cylverixxx]

Do you agree that Quantity A is just some number? If so, then it’s easy to eliminate D right off the bat.