We will focus on solving question 2a.
We are told that the parent function is
[tex]f(x)=x^2[/tex]we want to identify the transformations applied to this function so we get the function
[tex]g(x)=-x^2+4[/tex]Note first we can start by multiplyin f(x) by -1. So get
[tex]\text{ -f(x)= -x}^2[/tex]This multiplication by -1 represents a reflection across the x-axis. Now, if we add 4 to this equation, we get
[tex]\text{ -f(x) +4= -x}^2+4=g(x)[/tex]This move of adding 4 represent a shift of 4 units up.
So, to get the given function from the parent function, we should apply a reflection across the x-axis and the a shift of 4 units up