Quadratic Functions and Models: complete the square for 4x^2 - 4x + 21

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FritoTaco

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Hello,

I solved part of this question and I looked at the answer and it's not correct, but I followed the appropriate steps and I think I don't know something that I probably should. I use the completing the square method.

Equation: 4x^2 - 4x + 21

You can see my work in the attached file, (Sorry for the glare)

Also, the answer in the book is: h(x) = 4(x - 1/2)^2 + 20

I don't know where they got the 20.
 

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Well, I notice two errors. One, when completing the square, you go from:

\(\displaystyle \displaystyle x^2-x+\frac{1}{4}\) to \(\displaystyle \displaystyle (x-\frac{1}{2})\)

But you need to end up with \(\displaystyle \displaystyle (x-\frac{1}{2})^2\). Make sure you understand why that is. Two, you divided everything by 4 in order to get to the form x^2 + b + c, so you could complete the square. So, at the very end you're left with:

\(\displaystyle \displaystyle \frac{1}{4}h(x)=(x-\frac{1}{2})^2+5\)

So, you'd need to multiply both sides by 4 in order to get the true value of h(x), leaving you with the given answer.
 
Oh, yeah. I knew there needs to be a squared there I forgot to put it there. Also, that's why it's 20 because the 1/4 is still on the other side next to h(x), thank you very much!
 
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