If you take any shape, you can transform it:

5.1 Stretching/Reflecting Quadratic Relations

SQUARE

STRETCH IT

COMPRESS IT

TRIANGLESTRETCH

IT

COMPRESS IT

We can transform the shape of a parabola too:

Transforming Parabolas

y = x2 y = 9x2

STRETCHED

y = x2

COMPRESSED

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:

Transforming Parabolas

y = x2 y = -x2

When a < 0 (negative),

the parabola reflects over

the x-axis

Combining Both Transformations

y = x2 y = -9x2y = -x2

Standard Parabola Vertically StretchedReflected Over X-

Axis

Vertically Compressed

Reflected Over X-Axis

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…