We are given the equation y = 0.5x^2. To describe its transformation from (x, y) to (x, 4y), we can start by first graphing the given equation.
To graph, let's use sample points (x- and y-values):
x y
-2 2
-1 0.5
0 0
1 0.5
2 2
So we have the points (-2, 2), (-1, 0.5), (0, 0), (1, 0.5), and (2, 2) to help us graph the equation.
A transformation of (x, y) --> (x, ay) where a > 1 means a vertical stretch equal to |a|. In this case, because (x, y) is transformed to (x, 4y), the graph stretches vertically by a factor of 4.
To graph, let's use sample points (x- and y-values):
x y
-2 4(2) = 8
-1 4(0.5) = 2
0 4(0) = 0
1 4(0.5) = 2
2 4(2) = 8
The new graph would now look like this: