7J - Modelling with polynomial functions
Like all other functions that we have encountered so far, we can apply polynomial functions to model different situations.
7J - Example 1: Modelling the volume of an open box using polynomial functions (CAS)
A large rectangular piece of cardboard measuring 4 meters by 5 meters is to be turned into an open box by cutting squares, measuring \(x\) cm, from each of the four corners of the rectangle as shown. The sides of the box are then folded up to form the open box.
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7J - Example 1: Video solution
7J - Example 1: Practice
Question 1: ABC Question 2: ABC 7J - Example 1: Solutions
Question 1: ABC Question 2: ABC |
7J - Example 2: Modelling a rollercoaster using polynomial functions (CAS)
The first section of a rollercoaster can be modelled by the cubic function \[h(x)=\frac{1}{4}(x^3-15x^2+44x+60)\] where \(h\) is the height, in meters, of the roller coaster above the ground and \(x\) is the horizontal distance, in meters, from the starting platform of the ride. This function correctly models the rollercoaster for \(x\in [0,10]\).
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7J - Example 2: Video solution
7J - Example 2: Practice
Question 1: ABC Question 2: ABC 7J - Example 2: Solutions
Question 1: ABC Question 2: ABC |
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Worksheet A - Applying cubic functions (Technology Active)
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Worksheet B - Applying cubic functions (Technology Active)
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