EXPLANATION :
From the problem, we can see that the graph of g is to the right and below the graph of f.
We need to choose a specific point that is common between the two graphs.
For function f, we can choose the vertex (0, 0).
And in function g, the vertex is (3, -4)
We can compare the vertices :
The x-coordinate was translated from 0 to 3, so it moves 3 units to the right.
The y-coordinate was translated from 0 to -4, so it moves 4 units downward.
The translated function will be in the form :
[tex]g(x)=f(x-c)-d[/tex]
where c = number of units shifted to the right
d = number of units shifted downward.
So we have c = 3 and d = 4
The function will be :
[tex]g(x)=f(x-3)-4[/tex]
Note that f(x) is :
[tex]\begin{gathered} f(x)=x^2 \\ \text{ Then : }f(x-3)\text{ will be :} \\ \\ f(x-3)=(x-3)^2 \end{gathered}[/tex]
Then g(x) will be :
[tex]g(x)=(x-3)^2-4[/tex]
ANSWER :
g(x) = (x - 3)^2 - 4
