Maths Hubs Projects and Work Groups 2017-2018 Challenging Topics in the New GCSE NCP19-19 1) The cables of a suspension bridge form a parabolic shape above the bridge. These cables can be modelled by a quadratic graph. Such a model is shown below. All values in this model are in 10’s of metres. (a) The equation of this curve can be written in the form y = (x – a) 2 + b. From the graph above find the values of a and b and hence write down the equation of the curve. 2) A different bridge has cables spanning 80 metres. The closest the cables get to the bridge are 10 metres above the bridge. Similar to above, take each unit to represent 10 metres. (a) Find the equation of the cables curve in the form y = (x – a) 2 + b. You may find a sketch of the curve helpful. (b) By substituting x = 0 into your answer from (a) find the height of the supports for the cable at either end of the bridge Modelling with Quadratics (Pete Mattock)
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Maths Hubs Projects and Work Groups 2017-2018
Challenging Topics in the New GCSENCP19-19
1) The cables of a suspension bridge form a parabolic shape above the bridge. These cables can be modelled by a quadratic graph. Such a model is shown below.
All values in this model are in 10’s of metres.
(a) The equation of this curve can be written in the form y = (x – a)2 + b. From the graph above find the values of a and b and hence write down the equation of the curve.
2) A different bridge has cables spanning 80 metres. The closest the cables get to the bridge are 10 metres above the bridge. Similar to above, take each unit to represent 10 metres.
(a) Find the equation of the cables curve in the form y = (x – a)2 + b. You may find a sketch of the curve helpful.
(b) By substituting x = 0 into your answer from (a) find the height of the supports for the cable at either end of the bridge
3) The curve of a different bridge’s cables can be written in as y = x2 – 10x + 27. Express this in the form y = (x – a)2 + b. Hence find the minimum point of the cables.
Modelling with Quadratics (Pete Mattock)
Maths Hubs Projects and Work Groups 2017-2018
4) A basketball play shoots the ball to a hoop 4 metres away that is 1.2 metres higher than the ball as it leaves his hand. The ball travels in a parabolic curve and goes straight into the basket. This can be modelled by the curve below.
The equation of this curve is y = 4.3x – x2.
(a) Write this in the form y = -(x – a)2 + b.
(b) Hence write down the maximum height that the ball reaches and the distance away from the player when it reaches that height.
5) The basketball player thinks this model is unrealistic and proposes the equation . The graph of this is shown below.
(a) Write this in the form y = -a(x – b)2 + c.
(b) Write down the maximum height the ball reaches in the new model and the distance away from the player when the ball reaches this new maximum height.
