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Dilations of Quadratic Graphs - Problem
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
If there is a coefficient in front of x^2 in your quadratic function, then there is going to be either a vertical reflection, or a vertical stretch/compression, or possibly even both. Start by imagining or sketching the parent graph of y = x^2. then, if "a" is negative, then your parabola will open down- it gets reflected across the x-axis. If the absolute value of "a" is greater than one, then your parabola is going to get skinnier, which is called a vertical stretch. You can think of this in terms of how your outputs, or y's, are getting multiplied by some number, which will make the parabola steeper. If the absolute value of a is a fraction between 0 and 1, then your parabola is going to get wider, which is a vertical compression.
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