Answer:
(x - 2)² + 0
Step-by-step explanation:
Using x² - 4x + 4
(x² - 4x + 4)
x² - 4x + (-2)² - (-2)² + 4 (complete the square)
(x - 2)² - ( -2)² + 4 (use the binomial formula)
(x - 2)² + 0
Vertex point at (2,0)
Answer:
The answer is 24
Step-by-step explanation:
For each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes. Thus the sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is 6/36 = 1/6.
For this case we have the following functions:
![f (x) = 6x-1\\g (x) = 4x ^ 2 + x](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%206x-1%5C%5Cg%20%28x%29%20%3D%204x%20%5E%202%20%2B%20x)
We must find ![(g_ {o} f) (x):](https://tex.z-dn.net/?f=%28g_%20%7Bo%7D%20f%29%20%28x%29%3A)
By definition of composition of functions we have to:
![(g_ {o} f) (x) = g (f (x))](https://tex.z-dn.net/?f=%28g_%20%7Bo%7D%20f%29%20%28x%29%20%3D%20g%20%28f%20%28x%29%29)
So:
![(g_ {o} f) (x) = 4 (6x-1) ^ 2 + (6x-1) = 4 ((6x) ^ 2-2 (6x) (1) + (1) ^ 2) + 6x -1 = 4 (36x ^ 2-12x + 1) + 6x-1 = 144x ^ 2-48x + 4 + 6x-1 = 144x ^ 2-42x + 3](https://tex.z-dn.net/?f=%28g_%20%7Bo%7D%20f%29%20%28x%29%20%3D%204%20%286x-1%29%20%5E%202%20%2B%20%286x-1%29%20%3D%204%20%28%286x%29%20%5E%202-2%20%286x%29%20%281%29%20%2B%20%281%29%20%5E%202%29%20%2B%206x%20-1%20%3D%204%20%2836x%20%5E%202-12x%20%2B%201%29%20%2B%206x-1%20%3D%20144x%20%5E%202-48x%20%2B%204%20%2B%206x-1%20%3D%20144x%20%5E%202-42x%20%2B%203)
We have different signs subtracted and the sign of the major is placed.
Finally we have to:
![(g_ {o} f) (x) = 144x ^ 2-42x + 3](https://tex.z-dn.net/?f=%28g_%20%7Bo%7D%20f%29%20%28x%29%20%3D%20144x%20%5E%202-42x%20%2B%203)
ANswer:
![(g_ {o} f) (x) = 144x ^ 2-42x + 3](https://tex.z-dn.net/?f=%28g_%20%7Bo%7D%20f%29%20%28x%29%20%3D%20144x%20%5E%202-42x%20%2B%203)
Hello!
To tell if a function is increasing, it'll be going in an upwards direction. (Like /)
With this information, it'll be A & B.
Hope this helps! ☺♥