Graphs of Square Function
In this assignment different graphs of
for different values of a are examined.
The graph of
is a parabola, whose vertex is at (0,0).
The square function is an even function. The graph opens up when a>0, and
opens down when a<0. The line x = 0 is the axis of symmetry in this
By changing the coefficient a we
will be exploring the following cases:
Now, let us explore the above three cases
further. All three cases are demonstrated in the following graphs. Here
is the color key:
Case – 1: a>1, the graph of parabola
stretches toward y-axis
Case – 2: 0<a<1, the graph of
parabola shrinks toward x-axis
Case – 3: a<1, the graph of parabola
reflects about the x-axis.
The reflection of each one of the above
graphs across x-axis is when each graph has a negative coefficient.
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