Assignment # 2

By Sharren M. Thomas

In this exploration I will examine the graph y = ax2 on the same axes for different values of a.

For a = 1;         y = x2 is a parabola whose vertex is at the origin.  See the graph below.

For a = 2; y = 2x2 is a parabola whose vertex is at the origin, but the graph of the parabola is now stretched vertically by a factor of 2, each y-coordinate at each point has been multiplied by 2.  See both graphs below.

For a = 1/4      y = (1/4) x2 is a parabola whose vertex is at the origin, but the graph of the

parabola is now compressed vertically, each y – coordinate at each point

has been multiplied by 1/4.  See both graphs below.

Conclusion:

For y = ax2 with a> 1 the graphs will be parabolas whose vertices are at the origin that are stretched vertically by a factor of a.  Click the movie below.  Notice that the parabolas are becoming more narrow or sharper at the vertices.

For y = ax2 with 0 < a > 1 the graphs will be parabolas whose vertices are at the origin that are compressed vertically by a factor of a.  Click the movie below.  Notice that the parabolas are becoming wider or flatter at the vertices.

For a = -1;       y = -x2 is a parabola whose vertex is at the origin, but the graph of the parabola has been reflected across the x-axis.  Each y-coordinate of the new graph has been multiplied by -1.  See the graph below.

For y = ax2 with a < 0; the graphs will be parabolas whose vertices are at the origin that are reflected across the x-axis.  When a is a negative fraction it the graph is both reflected across the x-axis and compressed vertically by a factor of a.  Click the movie below.  Notice that the parabolas are becoming wider or flatter at the vertices.

For y = ax2 with a <0; the graphs will be parabolas whose vertices are at the origin that are reflected across the x-axis.  When a is a negative integer the graph is both reflected across the x-axis and stretched vertically by a factor of a.  Click the movie below.  Notice that the parabolas are becoming narrow or sharper at the vertices.