Question

The parent function f(x) = x2 is vertically compressed by a factor of 1/2 and translated 1 unit right and 3 units down to create g. Identify g in vertex form.

Answer 1

Since the function
`f(x)=x^2` is vertically compressed by a factor of 0.5 then the function is transformed in
`f_1(x)=(1)/(2)x^2`

Now,
`f_1(x)` is translated 1 unit right, obtaining the function
`f_2(x)=(1)/(2)(x-1)^2`

Then,
`f_2(x)` is translated 3 units down, obtaining the function

`g(x)=(1)/(2)(x-1)^2-3` that is in vertex form and the vertex of
`g(x)` is the point
`(1,-3)`