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• • Contributed by David Arnold
• Retired Professor (Mathematics) at College of the Redwoods
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• 5.1: The Parabola
In this section you will learn how to draw the graph of the quadratic function defined by the equation f(x)=a(x−h)2+k. You will quickly learn that the graph of the quadratic function is shaped like a "U" and is called a parabola. The form of this quadratic function is called vertex form, so named because the form easily reveals the vertex or “turning point” of the parabola. Each of the constants in the vertex form of the quadratic function plays a role.
• 5.2: Vertex Form
Once you have your quadratic function in vertex form, the technique of the previous section should allow you to construct the graph of the quadratic function. However, before we turn our attention to the task of converting the general quadratic into vertex form, we need to review the necessary algebraic fundamentals.
• 5.3: Zeros of the Quadratic
When drawing the graph of the parabola it is helpful to know where the graph of the parabola crosses the x-axis. That is the primary goal of this section, to find the zero crossings or x-intercepts of the parabola.