The basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.
To create a new parabola that resembles the fundamental parabola, we can translate the parabola vertically. The graph of the function y=x2+b simply resembles a regular parabola with the vertex moved b units down the y-axis. The vertex is so situated at (0,b). The parabola shifts upward if b is positive and downward if b is negative.
The parabola can also be translated horizontally. The graph of the function y=(x-a)^2 resembles a conventional parabola with the vertex moved one unit down the x-axis. then, the vertex is found at (a,0). Observe how we go to the right if an is positive and to the left if an is negative.
All parabolas can be obtained from the basic parabola by a combination of:
- translation
- reflection
- stretching
- rotation.
Thus, all parabolas are similar.
Hence the basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.
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