1. function and completing square

problem 1: re-arrange g(x) function below to completed square form
g(x)=-x^2+4x+1

I know the answer is 5-(x-2)^2

But how to get the answer? Mind to show steps?

problem 2: determine the turning point (x,y)
the answer is (2,5) but how to determine which term belongs to x or y ? does the term inside the brackets of square belong to x and the constant is y as a fixed rule?

thank you

2. Originally Posted by jasonmark
problem 1: re-arrange g(x) function below to completed square form
g(x)=-x^2+4x+1

I know the answer is 5-(x-2)^2

But how to get the answer? Mind to show steps?

problem 2: determine the turning point (x,y)
the answer is (2,5) but how to determine which term belongs to x or y ? does the term inside the brackets of square belong to x and the constant is y as a fixed rule?

thank you
$g(x) = -(x^2 -4x - 1) = -([x - 2]^2 - 2^2 - 1) = \, ....$

$y = a(x - h)^2 + k$ has a turning point at (h, k). In your question (whose answer can be re-written as $y = -(x-2)^2 + 5$), h = 2 and k = 5.

3. thank a lots