Question

Write a function based on the given parent function and transformations in the given order

Answer 1

Answer:

$y=-\left(x-2\right)^{2}-4$ is the resultant function after transformations.

Step-by-step explanation:

Parent function is given as:

$y=x^2$ (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 $x$ by 2.

The equation of a parabola can be: $y=(x-a)^2$ where $a$ is the point on x axis which is the axis of symmetry.

Right side means the equation becomes:

$y=(x-2)^2$  (Graph 2 in attachments)

2. Reflect over x axis i.e.

change the sign of y from + to -.

$y=-(x-2)^2$ (Graph 3 in attachments)

3. Shift downward 4 units i.e.

Subtract 4 from the value of y:

$y=-(x-2)^2-4$ (Graph 4 in attachments)