Understanding a completing the square question from the Quadratic functions & equations Unit Test.

I've come across similar scenarios multiple times during these tests and quizzes and I can get the correct answer but I do not understand it.

Consider a question from the Unit Test:

"Rewrite the equation by completing the square:

4x^2 - 4x + 1 = 0 "

The correct answer is (x-0.5)^2 = 0

My problem is that this isn't even the same parabola as the initial equation indicates. It may have the same vertex, and zeros, but the y intercept is completely different, and in fact, the entire curve is less divergent. The correct answer should be 4 (x-0.5)^2 = 0

My point is that from the so-called correct answer, you would have no idea what the original shape was unless you just happened to arbitrarily stick a lucky 4 in front of the (x-0.5)^2 term. So what is the point of a question that asks you to transform an initial state into something completely different? The answer really has no relation to the original equation. The answer should be 4 (x-0.5)^2 = 0

What am I not understanding about this answer?

Thanks,

John

mansab ali

May 11, 2020 10:18

hello JOHN

i am MANSAB ALI

First of all you had written the answer in two different places at the first position answer is wrong because (x-0.5)^2=0. Butt correct answer is that 4(x-0.5)^2=0

Solution:

4x^2 - 4x + 1 = 0

(2x)^2 - 2(2x)(1) + (1)^2 = 0 I write in this form a^2 - 2ab + b^2

(2x - 1)^2 = 0 By using identity a^2 - 2ab + b^2 = (a - b)^2

2^2(x - 1/2)^2 = 0 taking 2 common and also take the exponent on 2 . (ab)^m = a^m * b^m

4(x - 0.5)^2 = 0 2^2=4 and 1/2=0.5

Understanding a completing the square question from the Quadratic functions & equations Unit Test.

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