which function has a minimum and is transformed to the right and down from the parent function…

which function has a minimum and is transformed to the right and down from the parent function, $f(x)=x^{2}$?\n$g(x)=-9(x + 1)^{2}-7$\n$g(x)=4(x - 3)^{2}+1$\n$g(x)=-3(x - 4)^{2}-6$\n$g(x)=8(x - 3)^{2}-5$

which function has a minimum and is transformed to the right and down from the parent function, $f(x)=x^{2}$?\n$g(x)=-9(x + 1)^{2}-7$\n$g(x)=4(x - 3)^{2}+1$\n$g(x)=-3(x - 4)^{2}-6$\n$g(x)=8(x - 3)^{2}-5$

Answer

Explanation:

Step 1: Identify functions with a minimum

A function has a minimum if the coefficient (a > 0) in (g(x) = a(x-h)^2 + k).
Exclude (g(x) = -9(x + 1)^2 - 7) ((a = -9 < 0)) and (g(x) = -3(x - 4)^2 - 6) ((a = -3 < 0)).

Step 2: Check horizontal transformation

Right transformation requires (h > 0) (form (x - h)).
(g(x) = 4(x - 3)^2 + 1) has (h = 3) (right 3 units), (g(x) = 8(x - 3)^2 - 5) has (h = 3) (right 3 units).

Step 3: Check vertical transformation

Down transformation requires (k < 0).
(g(x) = 4(x - 3)^2 + 1) has (k = 1 > 0) (up 1 unit), (g(x) = 8(x - 3)^2 - 5) has (k = -5 < 0) (down 5 units).

Answer:

D. (g(x) = 8(x - 3)^2 - 5)