5.1 Stretching/Reflecting Quadratic Relations

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Presentation transcript:

5.1 Stretching/Reflecting Quadratic Relations If you take any shape, you can transform it: STRETCH IT COMPRESS IT SQUARE COMPRESS IT TRIANGLE STRETCH IT

Transforming Parabolas We can transform the shape of a parabola too: y = x2 y = 9x2 y = 𝟏 𝟗 x2 STRETCHED COMPRESSED

Transforming Parabolas 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 We can transform a parabola’s orientation too: When a < 0 (negative), the parabola reflects over the x-axis y = -x2 y = x2

Combining Both Transformations y = - 𝟏 𝟓 x2 y = x2 y = -9x2 Standard Parabola Vertically Stretched Reflected Over X-Axis Vertically Compressed Reflected Over X-Axis

In Summary… 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