The vertical translation depends on the sign of the constant that is being added.
The transformations are applied in an incorrect order and the translation is 4 units up, not down. The graph is obtained by reflecting the graph of y=x^2 across the x-axis and stretching it vertically by a factor of 6. Then, the resulting graph is translated up by 4 units.
Practice makes perfect
We want to describe and correct the error in the information we've been given. We will begin by noticing that the given function is a transformation of the form f(x)= a(x- h)^2+ k. Here a indicates a reflection in the x-axis and/or a vertical stretch or shrink, h indicates a horizontal translation, and k indicates a vertical translation.
f(x) = -6x^2+4
⇕
f(x) = -6(x- 0)^2 + 4
In our case, we have a= -6, h= 0 and k= -1. To obtain f(x)=-6x^2+4, we start from the parent function y=x^2 and follow the steps:
We reflect the graph across the x-axis and make a vertical stretch by a factor of 6. Here we get y= -6x^2.
We translate the graph obtained above 4 units up. Then we obtain f(x)= -6x^2+ 4.
As we can see in the given reasoning, the steps are not in the correct order. We need to start with the transformations represented by the constants a and h, and then finally we apply the transformation represented by k. Additionally, the translation is 4 units up, not down. In the following graph we can see each transformation.
Extra
Extra
If we apply the transformations described in the given reasoning we would get an erroneous graph, as we will show below.
Notice that the graph obtained was g(x)=-6x^2-4 which is different from f(x)=-6x^2+4.
