1. 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

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

3. 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

4. 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

5. 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

6. 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