if you take any shape, you can transform it: square stretch it compress it triangle stretch it...
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![Page 1: If you take any shape, you can transform it: SQUARE STRETCH IT COMPRESS IT TRIANGLE STRETCH IT COMPRESS IT](https://reader033.vdocuments.mx/reader033/viewer/2022051401/56649e975503460f94b9a9ae/html5/thumbnails/1.jpg)
If you take any shape, you can transform it:
5.1 Stretching/Reflecting Quadratic Relations
SQUARE
STRETCH IT
COMPRESS IT
TRIANGLESTRETCH
IT
COMPRESS IT
![Page 2: If you take any shape, you can transform it: SQUARE STRETCH IT COMPRESS IT TRIANGLE STRETCH IT COMPRESS IT](https://reader033.vdocuments.mx/reader033/viewer/2022051401/56649e975503460f94b9a9ae/html5/thumbnails/2.jpg)
We can transform the shape of a parabola too:
Transforming Parabolas
y = x2 y = 9x2
STRETCHED
y = x2
COMPRESSED
![Page 3: If you take any shape, you can transform it: SQUARE STRETCH IT COMPRESS IT TRIANGLE STRETCH IT COMPRESS IT](https://reader033.vdocuments.mx/reader033/viewer/2022051401/56649e975503460f94b9a9ae/html5/thumbnails/3.jpg)
What did we notice? If we consider parabolas to have the
equation y = ax2, then the standard parabola, y = x2 has a = 1◦ If a > 1, then the parabola is vertically stretched◦ If 0 < a < 1, then the parabola is vertically
compressed or horizontally stretched
Transforming Parabolas
![Page 4: If you take any shape, you can transform it: SQUARE STRETCH IT COMPRESS IT TRIANGLE STRETCH IT COMPRESS IT](https://reader033.vdocuments.mx/reader033/viewer/2022051401/56649e975503460f94b9a9ae/html5/thumbnails/4.jpg)
We can transform a parabola’s orientation too:
Transforming Parabolas
y = x2 y = -x2
When a < 0 (negative),
the parabola reflects over
the x-axis
![Page 5: If you take any shape, you can transform it: SQUARE STRETCH IT COMPRESS IT TRIANGLE STRETCH IT COMPRESS IT](https://reader033.vdocuments.mx/reader033/viewer/2022051401/56649e975503460f94b9a9ae/html5/thumbnails/5.jpg)
Combining Both Transformations
y = x2 y = -9x2y = -x2
Standard Parabola Vertically StretchedReflected Over X-
Axis
Vertically Compressed
Reflected Over X-Axis
![Page 6: If you take any shape, you can transform it: SQUARE STRETCH IT COMPRESS IT TRIANGLE STRETCH IT COMPRESS IT](https://reader033.vdocuments.mx/reader033/viewer/2022051401/56649e975503460f94b9a9ae/html5/thumbnails/6.jpg)
When compared with the graph of y = x2, the graph of y = ax2 is a parabola that has been stretched or compressed vertically by a factor ‘a’
When a > 1, graph is stretched vertically
When 0 < a < 1, graph is compressed vertically
If a > 0, parabola opens upward If a < 0, parabola opens downward
In Summary…