Question

Quadratic functions please help

Answer 1

Using the graph of f(x) = x2 as a guide, describe the transformations, and then graph the function. g(x) = 4.2x2

g is a vertical compression of f by a factor of 4.2

g is a horizontal stretch of f by a factor of 4.2

g is a vertical stretch of f by a factor of 4.2

g is a horizontal compression of f by a factor of 4.2

Answer 2

The quadratic function \[y=x^2\] is transformable in several ways.

Multiplying the right side of the equation by a constant value (e.g. 2) causes the resulting y values to be increased by that factor. \[y=2(x)^2\]This is also known as a vertical stretch. Of course, if the factor is less than one, then the graph actually shrinks- making the transform a vertical compression.

However, if you modify the coefficient of the x variable, something different happens:\[y= (2x)^2\] In this case, the graph is compressed by half. Think of it this way: What used to be a 1 is now a 2, what used to be a 2 is now a 4, and so forth. The graph moves twice as fast. As before, using a value of less than one causes the opposite effect- a horizontal stretch.

Generally speaking:\[y=A*(B*x)^2\] A > 1 --> vertical stretch
0 < A < 1 --> vertical compression
B > 1 --> horizontal compression
0 < B < 1 --> horizontal stretch

Negative values cause the graph to flip entirely, but that's beyond the scope of this question.