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.

c

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."