The phrase that best describes the translation from the graph of y = 6x² to the graph of y = 6x¹² is that it represents a vertical stretch along with a change in the degree of the polynomial.
To understand this better, let’s analyze both equations. The first equation, y = 6x², is a quadratic function, which means its graph is a parabola that opens upwards. The coefficient 6 indicates that the parabola is stretched vertically by a factor of 6.
On the other hand, the second equation, y = 6x¹², is a polynomial of degree 12. This means that while it also has a vertical stretch of 6, the graph will have a much steeper rise compared to the quadratic function. The higher degree affects the shape and steepness of the curve significantly, making it rise faster as x moves away from 0 in both positive and negative directions.
In conclusion, the transition from y = 6x² to y = 6x¹² is not only about the vertical scaling but also reflects a significant change in the overall behavior of the graph as a result of the change in the polynomial’s degree.