y=ax^2 is the equation that shows the vertical stertches and the compressions of a parabola. A represents the vertical stertch or compression of the parabola.
As you can see in the first
image (vertical stretch) the parabola that is formed is much narrower than the other parabola in the second (normal) and third (compression) image. We call this vertical stretch. A vertical stretch is taking the original y=x^2 and in a way stretching it so the width of the parabola is shorter and its vertical length is longer. vertical stretch occurs when the value of a is greater than -1 or 1. An equation that could represent a vertically stretched parabola might be something like y=2x^2 or y=-2x^2. In the second image (compression) the parabola that is formed is much wider than the first (vertical stretch) and the second (normal) parabola, it is much wider. We call this compression. Compression is taking the original y=x^2 and in a way squishing it, so the width of the parabola is wider and its vertical length is shorter. Compression occurs when the value of a is greater than 0 and less than 1. An equation that could represent a compressed parabola could be something like y=1/2 x^2. As you can see, the normal portrays the difference between the vertical stretch and compression at a greater extent. Also, the second image (normal) shows y= -x^2 graphed before any changes such as vertical stretch and vertical compression occur.
