Write y = x2 - 4x + 6 in vertex form.

y = (x-2)²  + 2

Step-by-step explanation:

Converting  y = x² - 4x + 6 in vertex form simply means converting from standard form y =  ax² - bx + c to the vertex form y = a(x-h)² + k

To start always check and make sure your a=1

In this equation our a=1

Next  is to find (b/2)²

(b/2)²  =  (-4/2)²  = (-2)²  = 4

Now we want to create a perfect square in our given equation, to do that we will add  the value of (b/2)² which is equal to 4 to the linear and quadratic term. That is;

y = x² - 4x + 6

y =( x² - 4x + 4) + 6

Since we added 4 into the parenthesis, we will subtract 4 outside the parenthesis to normalize the equation

y = (x² - 4x + 4) + 6 -4

We now have y = (x² - 4x + 4)  + 2  (1)

In the parenthesis we have: x² - 4x + 4 and this is a perfect square, think of the square that will give you this result, and that square is (x-2)²

We will now replace  x² - 4x + 4  by (x-2)²  in equation (1)

y = (x-2)²  + 2

Therefore  y = x2 - 4x + 6 in vertex form is y = (x-2)² + 2

there will be 35 boys in each team. : )

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.