Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x? ?
g(x) = -9(x + 1)2 - 7
og(x) = 4(x – 3)2 + 1
g(x) = -3(x – 4)2 - 6
g(x) = 8(x - 3)2 – 5

Option D.

Step-by-step explanation:

Note: The parent function is instead of .

Assume that the parent function is

The vertex of this function is (0,0).

The vertex form of a parabola is

where, a is a constant and (h,k) is vertex.

If a>0, then the function has minimum and if a<0, then the function has maximum.

It means if a function has minimum then the leading coefficient , must be positive.

The leading coefficient in option A and C are negative. So, option A and C are incorrect.

In option B, h=3, k=1. So, the vertex of the function is (3,1). It means the graph of parent function shifts 3 units right and 1 unit up.

In option D, h=3, k=-5. So, the vertex of the function is (3,-5). It means the graph of parent function shifts 3 units right and 5 units down.

Only, the function has a minimum and is transformed to the right and down from the parent function, .

Therefore, the correct option is D.