Algebra

Could you send another correctly tilted pic??

Then I could do it.

Hard to see this but I think we have 

a)    g(x)  = ( x + 2)^2  + 2

c)   g(−1 )   =  ( −1   + 2) ^2  + 2   =   1^2   + 2   =  3

Here's the graph  :  https://www.desmos.com/calculator/cacudo2xos

A- as you can see here, your function f is a referential equation: f(x)=x²

You can notice from the graph, let's call it the graph of the function g, is got by a translation of all the points of the graph of the  referential function f(x) = x² by a vector v(-2,2)

So, according to a theorem, the graph of a function \(x \rightarrow f(x+a)+b \)is got by a translation of the graph of \(x\rightarrow f(x)\)by using the vector v(-a,b)

As a result our function is \(g(x)=(x+2)²+2\)

g(-1) graphically = 3

g(-1) algebrically: g(-1) = (-1+2)²+2 = 1+2 = 3