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This second intercept has not yet appeared in the table above. The maximum area occurs when length and width are both 10 meters. This area is square meters. Notice that this rectangle has the same area as a rectangle with length 5 meters. Students could find the fixed perimeter by using clues from the table or graph. Or they might use the format of the equation to deduce the length and width.

Make a table and a graph for this equation. Estimate the price that will produce the maximum profit. How are the table and graph for this situation similar to those you made in Problem 1. How are they different? Students should recognize the format of this equation, even though the context has changed from areas of rectangles with fixed perimeters to profit.

They should be able to predict that the graph of this relationship will be a parabola. They may be able to predict where the maximum profit will occur, by examining the symbols. Get this Question solved. Get this solution now. Get notified immediately when an answer to this question is available.

You might want to try the quicker alternative needs Monthly Subscription No, not that urgent. Frogs, Fleas and Painted Cubes: Say It With Symbols: Making Sense of Symbols: Measuring Surface Area and Volume, Frogs Meet Fleas on a Cube: Describe the graph of this equation.

What is the maximum area for a rectangle with this perimeter? What dimensions correspond to this area? A rectangle with this perimeter has a length of 15 meters. What is its area? Describe 2 ways you can find the perimeter. What is the perimeter? In Investigation 1 students connected the equation for the areas of rectangles with fixed perimeters of 20 to the graph of the equation and to the table. They should recognize the format of the equation in this ACE question, and may be able to predict the shape of the graph and the fixed perimeter from the symbols.

If they are not able to do this yet they can still make a table from the equation, and proceed from there to a graph. The table would be: From the table we can predict that the graph will be a curve not a constant slope that will rise to a maximum when the length is This U shaped curve or parabola will cross the x-axis twice, at 0, 0 Document Preview: Jul 23 Get this Question solved Get a Tutor.

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Painted Cubes: Quadratic Relationships. In an earlier unit,Thinking With HELPING WITH HOMEWORK You can help with your child’s homework and encourage sound mathematical FROGS, FLEAS, AND PAINTED CUBES You can help your child with his or her work for this unit in several ways. Frogs, Fleas and Painted Cubes Introduction to quadratic equations In Frogs, Fleas and Painted Cubes, students build on their knowledge of linear and exponential functions to include the nonlinear polynomial relationship, which is the second-degree polynomial or the quadratic function.