1. Lesson 8

1.9. Explore 5

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

 

Modelling Problems with Quadratic Inequalities

 

The phrase “carbon footprint” refers to the amount of greenhouse gases produced through such activities as manufacturing a product or constructing a house. A carbon-neutral home or a zero-carbon home is a home where the net amount of carbon emissions from energy consumption over one year is 0. Such homes may be outfitted with geothermal heating and cooling features, solar energy panels, water conservation properties, and carbon-neutral building materials. Such homes are said to have a carbon-neutral footprint.

 

Did You Know?

This shows an illustration of a Tradical Hemcrete® block.

© The Freestead Project. Used with permission.

Tradical Hemcrete, an insulating bio-composite building material, is made of hemp, water, and a lime compound that holds everything together. Hemcrete is actually carbon-negative! In other words, the carbon dioxide emissions involved in the production of Hemcrete is more than compensated by the absorption of carbon dioxide in the growing and harvesting of the hemp plant.


Try This 5

 

Suppose the following graph shows the housing-price-to-construction-cost ratio of carbon-neutral homes for a Canadian city. The equation relates the housing-price-to-construction-cost ratio, y, of the number of years, x, since the year 2000. Here, 0 ≤ x ≤ 12.

 

This shows a graph of the house price to cost of construction ratio over 10 years since 2000. The equation of the graph is y = –0.024x2 + 0.277x + 1.01. It has a y-intercept of 1.01.


  1. Between what years was the housing-price-to-construction-cost ratio less than 1.5? Write an inequality that models the problem.

  2. Solve the inequality. Explain the strategy you used.

  3. The solution to the inequality from question 2 should be in the form of an interval. Interpret this interval.          

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Share 1

 

With a classmate, compare your answers to Try This 5. Discuss the following questions.

  1. What algebraic strategy or strategies may be appropriate to apply to this problem?

  2. How many different ways could you solve this problem graphically?

  3. How can this problem be modelled as a linear-quadratic system of equations?

course folder Save your responses in your course folder.