Which phrase best describes the translation from the graph y = 6x2 to the graph of y = 6(x+1)2?
Solution :
The function f(x) = 6x2 is a parabola having the vertex (0, 0) is translated one unit to the left which gives the equation y = 6(x+1)2
These equations can be compared with x2 = 4ay and (x - h)2 = 4a(y - k), where the first one represents a standard parabola whereas the second one represents a parabola whose axis is parallel to y-axis.
Also, we can say that the second kind of parabola is also obtained by shifting the position of the vertex of the first parabola i,e (0, 0) to new vertex (h, k) thus second equation is also called the equation of the shifted parabola which is obtained by shifting the vertex. The same transformation can be observed in the graph below.
Which phrase best describes the translation from the graph y = 6x2 to the graph of y = 6(x+1)2?
Summary:
The phrase best describes the translation from the graph y = 6x2 to the graph of y = 6(x+1)2 is that the vertex is shifted by 1 unit to the left.