Page 3b

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Summary of Graphing y = a(x - p)2 + q
The Effect of a
If a > 0, the parabola opens upward. If a < 0, the parabola opens downward. If |a| gets larger, the parabola becomes more narrow. If |a| approached zero, the parabola becomes wider. If |a| = 0, the graph is a horizontal line.
The Effect of p
If p > 0, the parabola is shifted right by p units from the origin. If p < 0, the parabola is shifted left by p units from the origin. NOTE: Since the parabola equation is y = a(x - p)2 + q, if p < 0, say p = -3, then the equation is y = a(x - (-3))2 + q = a(x + 3)2 + q.
The Effect of q
If q > 0, the parabola is shifted up by q units from the origin. If q < 0, the parabola is shifted down by q units from the origin.
The Vertex of the Parabola
Since the vertex of the parabola defined by y = x2 is the origin, (0, 0) and the values if p and q shift the graph as mentioned above, you can see then that the parbola defined by y = a(x - p)2 + q has its vertex at the point (p, q).

Once you have graphed a parbola, you easily answer some other common questions about a parabola, such as: What is the axis of symmetry? What is the domain? What is the range? What are the x-intercepts, if any exist? What are the y-intercepts, if any exist?

We answer these questions for the parabola in the example on page 3a, y = (1/4)(x - 6)2 + 3.

Answer the following questions which ask you to use the action figure to explore the roles played by the parameters a, p and q.