Help! Question 2 from "PrepSwift: Finding the Minimum Value" [3207]

[user8765]

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

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Hi everyone,

I am very lost on this, maybe i am missing something, but i don’t understand the given solution. Where is 1/2 and 1/4 coming from? Is it possible for someone to explain the solution using methodology/knowledge we learned in the corresponding prepswift video by Greg?

I guess because it is -x^2, that means its an upside down parabola so it will have a maximum value. But what i don’t understand is how we can deduce that minimum value is less than 1 from that.

Thanks!

[Kweku]

Hi @user8765

@user8765

Where is 1/2 and 1/4 coming from?

It is from Completing the square

@user8765

I guess because it is -x^2, that means its an upside down parabola so it will have a maximum value

Yes

@user8765

But what i don’t understand is how we can deduce that minimum value is less than 1 from that.

Since |x| ≤ 10⁷, substitute 10⁷ into Qa. That’s how we get -10¹⁴