To get the equations of the graph we proceed as follows:
The vertex form of equation is given by:
f(x)=(x-k)^2+h
where (k,h) is the vertex.
a] Graph A
From the graph, our vertex is at (-3,-4), substituting this in our formula we get the equation will be:
f(x)=(x+3)^2-4
b] Graph B
From the graph, the vertex is (-4,-3), substituting the values in our equation we get the equation of the graph to be:
f(x)=(x+4)^2-3
Answer: f(x)=(x+4)²-3
c] Graph C
From the graph, the vertex is at point (3,4); thus substituting our values in the vertex form of the equation we get:
f(x)=(x-3)²+4
Answer: f(x)=(x-3)²+4
d] Graph D
From the graph, the vertex is at point (4,3); substituting the values in our formula we get:
f(x)=(x-4)²+3
Thus the answer is: f(x)=(x-4)²+3