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

We have the equation:

h (x) = 4 x² - 16

When shifted 5 units right:

h (x) = 4 (x - 5) ² - 16

And shifted 2 units down:

h (x) = 4 (x - 5) ² - 16 - 2 = 4 (x - 5) ² - 18

Answer:

The new equation is: h (x) = 4 (x - 5) ² - 18.