If g (x) = 4x2-16 were shifter 5 units to the right and 2 down, what would the new equation be?

G (x) = 4x^2-16

To shift to the right we have to subtract from the value of x, in this case by 5 units ...

h (x) = 4 (x-5) ^2-16

h (x) = 4 (x^2-10x+25) - 16

h (x) = 4x^2-40x+100-16

h (x) = 4x^2-40x+84

Now to shift the function downwards by 2 units we must subtract the constant 2 from h (x)

h (x) = 4x^2-40x+84-2

h (x) = 4x^2-40x+82