Lesson37 - MA 15200 Lesson 37, Sections 3.1 and Appexdix H...

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MA 15200 Lesson 37, Sections 3.1 and Appexdix H If a parabola opens downward, the vertex is the highest point of the graph. The y - coordinate of that vertex is the largest value in the range of the function. That y - coordinate value is called the maximum of the function or equation and that maximum occurs when x = h . There are several real life applications where a maximum value can be found by writing an equation for a parabola and finding its vertex. It is important when solving these applied problems that you understand what ‘label’ the h and the k of the vertex represent. Examine the following quadratic functions. 2 ( ) 0.02 4 12 P x x x = - + + Each ordered pair is of the form ( , ) x P or (# items, profit) The above function represents profit for a week based on the number of items x made and sold. After the vertex ( , ) h k is found, the h represents the number of item made and sold to get a maximum profit. The k is that maximum profit. 2 ( ) 2 650 A w w w = - + and 650 2 L w = - Each ordered pair is of the form ( , ) w A or (width, area). The above function represents the area of a rectangular region where
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Lesson37 - MA 15200 Lesson 37, Sections 3.1 and Appexdix H...

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