Parabolas and Graphing functions

Question

Let the graph of g be a translation 6 units right and 8 units up, followed by a reflection in the x-axis of the graph f(x)=x^2 - 4x.

Write a rule for g.

Answer 1

Translating 6 units to the right and 8 units up gives y = (x+6)² - 4(x+6) + 8 = (x+6)² - 4x - 16

Reflect in the x-axis to get g(x) = -(x+6)² + 4x + 16