Quadratic Transformations - Tying it together

A.7C offers a new twist on an old idea.

Parabolas still move up and down, but they also move left and right now.

They still get narrower and wider, but we also describe those changes as compressions and stretches. And while the old standards only included vertical stretches and compressions, the new standards discuss horizontal stretches and compressions.

Distinguishing between horizontal compressions and vertical stretches is tricky. Take a look at this example:

Horizontal Compression: f(x) = (2x)^2  

Vertical Stretch: f(x) = 2x^2

Both of these transformations will result in a graph that is narrower than the parent function. An important difference to notice is that the narrowing effect of the horizontal compression will be stronger than that of the vertical stretch since the "a" coefficient of the compression is squared.

One more point to keep in mind: a horizontal compression of f(x) = (2x)^2 is equivalent to a vertical stretch of f(x) = 4x^2! The effect on the graph of the parabola will be exactly the same; we can only distinguish between the two when we look at the value and placement of the coefficient in the equation.