Sec 35-filled-2 - Math 1310 Section 3.5 Maximum and Minimum...

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Math 1310 Class Notes – Section 3.5, Page 1 of 5 Math 1310 Section 3.5 Maximum and Minimum Values Next, we’ll look at a specific type of function, the quadratic function. A quadratic functionis a function of the form ,)(2cbxaxxf++=where a, band care real numbers and 0a. We can write a quadratic function in the form khxaxf+-=2)()(. This is called the standard or vertex form of the quadratic equation. The graph of a quadratic function is a parabola with vertex ),(kh. It will open either upward or downward. If it opens upward, it has a minimum value k. If it opens downward, it has a maximum value k. We can use the graph of the quadratic function to help us find the maximum or minimum value of the function. Our first task will be to change a given quadratic function from the form cbxaxxf++=2)(to standard form. We’ll complete the square to do this. Once the function is in standard form, we can sketch a graph using transformations and then read off the maximum or minimum value.

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