Answer:
A. y= 2(x - 2)2 + 4
Step-by-step explanation:
vertex having an x value of 2 means the phrase in paren must be x - 2.
This eliminates B and D
vertex having a y value of 4 is of no help as the remaining two equations will result in 4 if the x term is 2
plugging in x = 3 makes y = 6 in equation A, but not in equation C where y = 10
Answer:


Step-by-step explanation:
Given



Required
Find P(A) and P(B)
We have that:
--- (1)
and
--- (2)
The equations become:
--- (1)

Collect like terms


Make P(A) the subject

--- (2)


Substitute: 
![[0.770 - P(B)] * P(B) = 0.144](https://tex.z-dn.net/?f=%5B0.770%20-%20P%28B%29%5D%20%2A%20P%28B%29%20%3D%200.144)
Open bracket

Represent P(B) with x

Rewrite as:

Expand

Factorize:
![x[x - 0.45] - 0.32[x - 0.45]= 0](https://tex.z-dn.net/?f=x%5Bx%20-%200.45%5D%20-%200.32%5Bx%20-%200.45%5D%3D%200)
Factor out x - 0.45
![[x - 0.32][x - 0.45]= 0](https://tex.z-dn.net/?f=%5Bx%20-%200.32%5D%5Bx%20-%200.45%5D%3D%200)
Split

Solve for x

Recall that:

So, we have:

Recall that:

So, we have:


Since:

Then:


That's the easily recognizable factored form of
the difference between two squares. Before
factoring, it was
x² - 16 .