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6.6 optimization

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Optimization is the process of finding the best way to do something, such as the maximum or minimum value of a quadratic function. For a function modeling popcorn popping volume with moisture content as a percent of weight, the moisture content that maximizes volume and the maximum volume itself can be found by graphing the function on a calculator and locating the vertex.

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6.6 Optimization
What is Optimization? A process used to find the “best” way to do something. For quadratic functions, this will occur at the maximum or minimum value of the function. The max/min occurs at the vertex.
Finding Max/Mins We will use graphing calculators! 1. Graph the function. 2. Fix window. 3. Find vertex.
Example:  A kernel of popcorn contains water that expands when the kernel is heated, causing it to pop. The equation below gives the “popping volume” y (in cubic centimeters per gram) of popcorn with moisture content x (as a percent of the popcorn’s weight).  What moisture content maximizes popping volume?  What is the maximum volume?

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6.6 optimization

  • 2. What is Optimization? A process used to find the “best” way to do something. For quadratic functions, this will occur at the maximum or minimum value of the function. The max/min occurs at the vertex.
  • 3. Finding Max/Mins We will use graphing calculators! 1. Graph the function. 2. Fix window. 3. Find vertex.
  • 4. Example:  A kernel of popcorn contains water that expands when the kernel is heated, causing it to pop. The equation below gives the “popping volume” y (in cubic centimeters per gram) of popcorn with moisture content x (as a percent of the popcorn’s weight).  What moisture content maximizes popping volume?  What is the maximum volume?