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QUADRATIC FUNCTIONS: QUESTIONS AND ANSWERS We usually write the defining equation for a quadratic function in one of two useful forms. These are: Standard form: 2 ( ) ( 0) f x ax bx c a = + + Vertex form: 2 ( ) ( ) ( 0) f x a x h k a = - + We may ask a number of questions about a given quadratic function. The means used to obtain the answers often depend on the form in which the defining equation is written. Because of this, we shall place questions in the middle of the page, and provide most answers twice; once on the left side of the page (for use if the function is given in standard form), and once on the right side of the page (for use if the function is given in vertex form). Also, we shall use y and ( ) f x interchangeably here, even though they technically have different meanings. Plotting the graph of a quadratic function always results in a non-linear curve whose shape is called a “parabola.” Q. How do I tell whether the parabola’s arms open upward (“happy”) or downward (“unhappy”)? Also, how do I determine whether the parabola has a maximum or a minimum?
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