SOLUTION: The Pedestrian Bridge over the Yarra River is a bow truss construction and the curve of the arch is a parabola. The length of the bridge is 45.7 metres and the height of the arch i

Question 915298: The Pedestrian Bridge over the Yarra River is a bow truss construction and the curve of the arch is a parabola. The length of the bridge is 45.7 metres and the height of the arch is 10.65 metres. The rule I was given is y=a(x+h)�+k.
What is the value of a, h and k?
How would I draw this parabola on a graph?
Thanks
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The general formula of a parabola is given by your example (note (x-h) NOT (x+h),
y = a(x-h)^2 + k where the point (h,k) is the vertex
we are given the length of the bridge is 45.7 m and height is 10.65, therefore
h = 45.7/2 = 22.85
k = 10.65
so far we have
y = a(x-22.85)^2 + 10.65
we have two x intercepts, (0,0) and (45.7, 0)
let's use (0,0) to find our value for a
0 = a(0-22.85)^2 +10.65
0 = a522.1225 +10.65
a522.1225 = -10.65
a = -10.65 / 522.1225 = −0.020397512 which is approx -0.02
now we have
y = -0.02(x-22.85)^2 + 10.65
y = -0.02x^2 +0.02*45.7x + -0.02*522.1225
y = -0.02x^2 +0.914x -10.44245 +10.65
y = -0.02x^2 +0.914x +0.20755
it's graph looks like

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