A.6.15.3 Playing with Parameters

Using graphing technology, graph y = x². Then, add different numbers to before it is squared (for example, y = (x +4)² or y = (x - 3)²) and observe how the graph changes.[br][br]Record your observations.
Graph y = (x - 1)². Then, experiment with each of the following changes to the function and see how they affect the graph and the vertex:[br][br]a. Adding different constant terms to y = (x - 1)² (for example: y = (x - 1)² + 5 or y = (x - 1)² - 9).[br]b. Multiplying y = (x - 1)² by different coefficients (for example: y = 3(x - 1)² or y = -2(x - 1)²).
Without graphing, predict the coordinates of the vertex of the graphs of these quadratic functions, and predict whether the graph opens up or opens down. Ignore the last row for now.[br][br]Use graphing technology to check your predictions. If they are incorrect, revise them.[br]Then, complete the last row of the table.
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– Katie Akesson

Information: A.6.15.3 Playing with Parameters