Question

Identify the transformations of the function g(x)=-½(x-6)2+3 compared to the parent function f(x)=x2

Answer 1

If
`f(x)=x^2` and
`g(x) = -(1)/(2)(x-6)^2 + 3`,

then:

1. the negative is a reflection over the x-axis.
2. the
   `(1)/(2)` is a vertical compression by a factor of 1/2
3. the
   `{}-6` shifts the graph 6 units to the right
4. the
   `{}+3` shifted the graph up by 3 units.

So the graph has been flipped upside-down, squished vertically, moved right and up.