Answer:
[tex]y=-\left(x-2\right)^{2}-4[/tex] is the resultant function after transformations.
Step-by-step explanation:
Parent function is given as:
[tex]y=x^2[/tex] (Graph 1 in attachments, it is a parabola)
Let us apply the transformations step by step:
1. Shift 2 units to the right i.e.
change the value of [tex]x[/tex] by 2.
The equation of a parabola can be: [tex]y=(x-a)^2[/tex] where [tex]a[/tex] is the point on x axis which is the axis of symmetry.
Right side means the equation becomes:
[tex]y=(x-2)^2[/tex] (Graph 2 in attachments)
2. Reflect over x axis i.e.
change the sign of y from + to -.
[tex]y=-(x-2)^2[/tex] (Graph 3 in attachments)
3. Shift downward 4 units i.e.
Subtract 4 from the value of y:
[tex]y=-(x-2)^2-4[/tex] (Graph 4 in attachments)
