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

step-by-step explanation:

t hope this

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