Describe the translation.
y=(x−5)2+5 → y=(x−0)2+0
see earlier post
better yet, graph the two functions and see the shifts
To describe the translation from the first equation to the second equation, we can analyze the changes made to the variables.
In the first equation, y=(x−5)^2+5, we have a horizontal translation.
- The term (x-5) represents a shift of 5 units to the right. This means the graph of the equation is moved to the right by 5 units.
- The term +5 represents a vertical translation. It shifts the graph upwards by 5 units.
In the second equation, y=(x−0)^2+0, we notice two changes:
- The term (x-0) represents no horizontal translation since it simplifies to (x), meaning it remains the same as the original x.
- The term +0 represents no vertical translation, as adding 0 to a value does not change the value.
So, the translation from the first equation to the second equation can be described as no horizontal translation and no vertical translation. The graph remains in its original position.