Where did the 9/4 come from? y = x^2 + 3x + 5
= ( x^2+3x ) +5
= (x^2 +3x + 9/4 ) - 9/4 +5
= (x + 3/2)^2 +11/4

( I already asked this question but someone literally answered it with an 'f' so i couldn't get an answer in the end :/ )

Ok so this concept is kind of hard to explain, but basically the two equations are equal because you are adding 9/4 and then subtracting 9/4, so you just end up with 0. The reason you do that is so you can make the (x + 3/2)^2 part, which you wouldn't be able to do without the 9/4/

When changing something to Vertex form you have the, in this case, coefficient to 3x which is 3 then square it. So you half it to 3/2 then square the fraction which becomes 9/4. Because you are adding the 9/4 in order to make this a perfect square you have to subtract it on the outside too leaving you with the answer provided.

In short:

When changing to stand form you need to half and square the X term to get the x intercept.

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.

ok thats very interesting