4K - Modelling with quadratic equations
The skills developed so far in this section can be used to model different ‘real-world’ problems where the relationship between two variables is quadratic, such as the flight path of an object or the shape of a bridge.
4K - Example 1: Modelling the flight of an object with quadratic functions
Jeremy throws a ball up into the air. The height (in meters) of the ball, after \(t\) seconds, can be modelled by the function: \(h(t)=-0.15t^2+2.1t+2.25\)
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4K - Example 1: Video solution
4K - Example 1: Practice
Question 1: ABC Question 2: ABC 4K - Example 1: Solutions
Question 1: ABC Question 2: ABC |
4K - Example 2: Optimisation using quadratic functions
Geordie has 1600 meters of fencing available and wants to fence off a rectangular paddock which boarders a straight river; as such no fence is needed along this stretch.
What are the dimensions of the largest possible paddock?
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4K - Example 2: Video solution
4K - Example 2: Practice
Question 1: ABC Question 2: ABC 4K - Example 2: Solutions
Question 1: ABC Question 2: ABC |
4K - Example 3: Modelling the area of a shape using quadratic functions
A pool with a concrete path surrounds it is shown in the diagram below. All measurements are in meters.
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4K - Example 3: Video solution
4K - Example 3: Practice
Question 1: ABC Question 2: ABC 4K - Example 3: Solutions
Question 1: ABC Question 2: ABC |
4K - Example 4: Modelling the shape of a bridge using quadratic functions (CAS)
A bridge is a parabolic shape which can be modelled by the quadratic equation \[H=-\frac{1}{5}x^2+4x\] where \(H\) is the height (in meters) above a river and \(x\) is the horizontal distance (in meters).
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4K - Example 4: Video solution
4K - Example 4: Practice
Question 1: ABC Question 2: ABC 4K - Example 4: Solutions
Question 1: ABC Question 2: ABC |
4K - Example 5: Modelling flight paths with quadratic equations
Amy jumps directly out from the diving tower at Eastern Beach. Her path through the air can be modelled by the quadratic equation \(h=-d^2+4\), where \(h\) represents the height (in meters) above sea level and \(d\) represents the horizontal distance away from the tower (in meters).
Laura is also at Eastern Beach with Amy. Instead of jumping directly out from the tower, Laura jumps further into the air before falling to the water. Laura’s flight path through the air can be modelled by the quadratic equation \(h=-2(d^2-d-2)\) where \(h\) represents the height (in meters) above sea level and \(d\) represents the horizontal distance (in meters) away from the tower.
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4K - Example 5: Video solution
4K - Example 5: Practice
Question 1: ABC Question 2: ABC 4K - Example 5: Solutions
Question 1: ABC Question 2: ABC |