The graph of y = ax² is a parabola, whose vertex is at (0,0)

Assignment 2

Exploring Graphs of Square Function

Behnaz Rouhani

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 case.

By changing the coefficient a we will be exploring the following cases:

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.

Now, let us explore the above three cases further. All three cases are demonstrated in the following graphs. Here is the color key:

The reflection of each one of the above graphs across x-axis is when each graph has a negative coefficient.

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