Question

Which function has a minimum and is transformed to the right and down from the parent function, (f(x)=x²)?

a) (g(x)=-9(x+1)²-7)
b) (g(x)=4(x-3)²+1)
c) (g(x)=-3(x-4)²-6)
d) (g(x)=8(x-3)²-5)

Answer 1

The function that has a minimum and is transformed to the right and down from the parent function f(x) = x² is g(x) = -3(x-4)²-6.

Step-by-step explanation:

To determine the correct function, we need to consider the transformations applied to the parent function f(x) = x². The parent function has a minimum at (0,0). The given options are:

1. (g(x)=-9(x+1)²-7)
2. (g(x)=4(x-3)²+1)
3. (g(x)=-3(x-4)²-6)
4. (g(x)=8(x-3)²-5)

The transformation that shifts the function to the right and down would be the option that has a negative value in the brackets (x+a) and a negative value outside the brackets. This corresponds to option c) (g(x)=-3(x-4)²-6).