Answer:
(-1,-6)
Step-by-step explanation:
We have the following function:
![f(x) = x^{2} + 6x + 3](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E%7B2%7D%20%2B%206x%20%2B%203)
The following transformation is applied
![g(x) = f(x - 2)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x%20-%202%29)
So
![g(x) = f(x - 2) = (x - 2)^{2} + 6(x - 2) + 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28x%20-%202%29%20%3D%20%28x%20-%202%29%5E%7B2%7D%20%2B%206%28x%20-%202%29%20%2B%203)
![g(x) = x^{2} - 4x + 4 + 6x - 12 + 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E%7B2%7D%20-%204x%20%2B%204%20%2B%206x%20-%2012%20%2B%203)
![g(x) = x^{2} + 2x - 5](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E%7B2%7D%20%2B%202x%20-%205)
For a second order function in the format:
![g(x) = ax^{2} + bx + c](https://tex.z-dn.net/?f=g%28x%29%20%3D%20ax%5E%7B2%7D%20%2B%20bx%20%2B%20c)
The vertex is:
![V = (x_{v}, g(x_{v})](https://tex.z-dn.net/?f=V%20%3D%20%28x_%7Bv%7D%2C%20g%28x_%7Bv%7D%29)
In which
![x_{v} = -\frac{b}{2a}](https://tex.z-dn.net/?f=x_%7Bv%7D%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
In this problem
![a = 1, b = 2](https://tex.z-dn.net/?f=a%20%3D%201%2C%20b%20%3D%202)
So
![x_{v} = -\frac{2}{2*1} = -1](https://tex.z-dn.net/?f=x_%7Bv%7D%20%3D%20-%5Cfrac%7B2%7D%7B2%2A1%7D%20%3D%20-1)
Then
![g(x_{v}}) = g(-1) = (-1)^{2} +2(-1) - 5 = -6](https://tex.z-dn.net/?f=g%28x_%7Bv%7D%7D%29%20%3D%20g%28-1%29%20%3D%20%28-1%29%5E%7B2%7D%20%2B2%28-1%29%20-%205%20%3D%20%20-6)
So the correct answer is:
(-1,-6)
Answer:
The given situation can be modeled by a simulation that has 8 different possible outcomes and each outcome has the same probability of occurrence. Design a spinner having 8 equal sections and label each section with a different sports card.
Step-by-step explanation:
A sports company randomly sends out various cards of 8 different sports.
We are asked to describe a model that could be used to simulate which sport would be sent out.
The given situation can be modeled by a simulation that has 8 different possible outcomes and each outcome has the same probability of occurrence.
Design a spinner having 8 equal sections and label each section with a different sports card.
Therefore, by spinning the spinner, we can randomly select a sports card that should be sent out from a total of 8 sport cards.
The simulation may be repeated as per the required number of times.
Answer:
25.5
Step-by-step explanation:
Hope this helps!
Check the picture below.
surely you can solve for "v", right?