Question

A quadratic function f(x) has been transformed using g(x) =kf(x) and k=-2. What effect does the transformation haye on f(x) ?

Answer 1

The transformation g(x) = -2f(x) reflects the graph of f(x) across the x-axis and stretches it vertically by a factor of 2.

Step-by-step explanation:

When a quadratic function f(x) is transformed using the function g(x) = kf(x) with k = -2, it means that the function g(x) is a reflection of the original function f(x) across the x-axis. The negative value of k (-2) indicates that each point on the graph of f(x) will be reflected downward by a factor of 2 units.

For example, if the vertex of the parabola representing f(x) is (2, 3), the corresponding vertex of g(x) will be (2, -6). The shape of the parabola remains the same, but it is reflected downward.

So, the transformation g(x) = -2f(x) reflects the graph of f(x) across the x-axis and stretches it vertically by a factor of 2.