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Sydney Harbour Bridge Investigation

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Sydney Harbour Bridge – Directed Investigation – Quadratic functions
Introduction:
Aim: To find the multiple unknowns in the Sydney Harbour bridge
The Sydney Harbour Bridge will be used to investigate a diverse number of points in the structure such as the height and length. Quadratics will be used to solve the height of the bridge at different points on the x axis.
A quadratic is an equation constructed from information collected from a graph; this equation can also be used to produce a graph. Quadratics can be used to solve the problem dealt in this investigation as the Sydney Harbour Bridge is identified as a parabola shape. Only basic information is given about the bridge and the answers can be established by solving the additional questions. The quadratic equation will be tested from the graph to prove the accuracy of the quadratic identified. Quadratics are mainly seen in the form ax^2+bx+c=0, where x is a variable of any number.
The bridge is mounted on two base pylons on the opposite ends. The highest point of the bridge is 182.5cm above sea level and the longest vertical cable is 135m from the origin. This position is the vertex, which is the highest or lowest point inside a quadratic, and in this case it is highest in this scenario. The axis of symmetry is an imaginary vertical line that cuts through and splits both sides evenly on the graph. The main supporting arc has 2 points that sits on the road situated 50m above sea level.
Mathematical Investigations:
The bridge is supported by two pylons at both ends of the bridge, if the bases of the pylons are at sea level, the width can be found using the mid-point of the x axis. Due to the fact that the base pylons are at the end of each bank, by multiplying the midpoint by two, the total width of the sea level can be identified.
Width of sea level:
Midpoint x 2 = xm
135 x 2 = xm
Width of sea level =

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