By analysing graph and then checking for all options we got that graph represent the function F(x) = -3(x +1)^2+ 2
<h3>What is function ?</h3>
Function is a relation from one set to another with a property that every element of a first set has a unique image in second set.
Here by looking at graph we can say that graph is if a quadratic equation
and it passes through (0,-1) and also from (-1,2)
Now we will check all options
(1)
Given function is
![F(x) = 3(x +1)^2+ 2](https://tex.z-dn.net/?f=F%28x%29%20%3D%203%28x%20%2B1%29%5E2%2B%202)
Put x=0
![F(0) = 3(0+1)^2+ 2=3+2=5](https://tex.z-dn.net/?f=F%280%29%20%3D%203%280%2B1%29%5E2%2B%202%3D3%2B2%3D5)
This function not passes through point (0,-1)
(2)
Given function is
![F(x) = -3(x +1)^2+ 2](https://tex.z-dn.net/?f=F%28x%29%20%3D%20-3%28x%20%2B1%29%5E2%2B%202)
Put x=0
![F(0) = -3(0+1)^2+ 2=-3+2=-1](https://tex.z-dn.net/?f=F%280%29%20%3D%20-3%280%2B1%29%5E2%2B%202%3D-3%2B2%3D-1)
Put x= -1
![F(-1) = -3(-1 +1)^2+ 2=0+2=2](https://tex.z-dn.net/?f=F%28-1%29%20%3D%20-3%28-1%20%2B1%29%5E2%2B%202%3D0%2B2%3D2)
This function passes through both points (0,-1) and (-1,2)
(3)
Given function is
![F(x) = -3(x +1)^2- 2](https://tex.z-dn.net/?f=F%28x%29%20%3D%20-3%28x%20%2B1%29%5E2-%202)
Put x= -1
![F(-1) = -3(-1 +1)^2-2=0-2=-2](https://tex.z-dn.net/?f=F%28-1%29%20%3D%20-3%28-1%20%2B1%29%5E2-2%3D0-2%3D-2)
This function not passes through point (-1,2)
(4)
Given function is
![F(x) = 3(x +1)^2+ 2](https://tex.z-dn.net/?f=F%28x%29%20%3D%203%28x%20%2B1%29%5E2%2B%202)
Put x=0
![F(0) = 3(0+1)^2+ 2=3+2=5](https://tex.z-dn.net/?f=F%280%29%20%3D%203%280%2B1%29%5E2%2B%202%3D3%2B2%3D5)
This function not passes through point (0,-1)
By analysing graph and then checking for all options we got that graph represent the function F(x) = -3(x +1)^2+ 2
To learn more about function visit : brainly.com/question/25638609