Question

Fully describe the translation from

�
=
�
2
y=x
2
to
�
=
�
2
+
6
y=x
2
+6.
Give your answer in vector form.

Answer 1

The translation from y = x^2 to y = x^2 + 6 in vector form is represented by <0, 6>, or equivalently, 0i + 6j, reflecting a vertical shift upwards by 6 units.

Step-by-step explanation:

The translation of the function y = x^2 to y = x^2 + 6 can be described in vector form. A translation in the positive y-direction by 6 units is represented by the vector <0, 6>. To express this using unit vectors, it would be 0i + 6j as the unit vector i points horizontally to the right and the unit vector j points vertically upward.

The original function does not move along the x-axis, hence the x-component of the translation vector is 0. The y-component of the vector is +6, indicating a shift of 6 units upwards along the y-axis. Therefore, the full vector describing the translation is 0i + 6j.