Describe the transformations.
1. g(x)=(2x)^2
2. g(x)=-1/2x^2
if f(x) = x^2,
1. scale by 4 in y direction
or, scale by 1/2 in x direction
2.
scale by 1/2 in y direction
reflect in x-axis
I mean is it vertically/horizontally stretched/compressed? By what factor?
To describe the transformations in the given function expressions, we need to understand the general form of a quadratic function: g(x) = a(x - h)^2 + k. In this form, (h, k) represent the coordinates of the vertex, and 'a' determines the direction and degree of scaling of the graph.
1. g(x) = (2x)^2:
This expression can be simplified to g(x) = 4x^2. Comparing it to the general form, we can see that 'a' is equal to 4, which means the graph is vertically stretched by a factor of 4 compared to the default parabola. The vertex (h, k) is located at (0, 0), implying that there is no horizontal shift or vertical shift in this case.
2. g(x) = -1/2x^2:
In this expression, 'a' is equal to -1/2. This means that the graph is vertically flipped compared to the standard parabola (upside down), and it is also compressed by a factor of 1/2. The vertex (h, k) is still located at (0, 0), indicating no horizontal shift or vertical shift.
By understanding the general form of a quadratic function and comparing the given expressions, we can determine the transformations applied to the default parabola.