F(x)=x^2: Stretch vertically by a factor of 2 and reflect in the x-axis

Question

Write and equation for the final tranformed graph

Answer 1

f(x) = x²

The transformations are:

g(x) = a·(b(x-c))² + d

1. a = vertical stretch. If a<0, reflects graph across x -axis
2. b = horizontal stretch. If b<0, reflects graph across y-axis
3. c = horizontal shift
4. d = vertical shift

You want to stretch vertically by a factor of 2 and reflect across the x-axis, so a = -2. You're not doing anything else so b = 1 and c and d = 0.

g(x) = -2x²