Problema Solution
a parabolic arch spans 30 meters and has a maximum height of 10 meters. Derive the equation of the arch, using the vertex of the arch as the origin.
Answer provided by our tutors
the general equation of parabola with axes of symmetry parallel to the y-axis is
y = ax^2 + bx + c
the x-coordinate at the vertex is x=-b/2a
since we are using the vertex as origin we have -b/2a = 0 => b = 0
the parabola is passing trough the points O(0,0,), A(-30, -10) an B(30, -10)
substitute O(0,0,) in y = ax^2 + c we get 0 = a*0^2 + c => c=0
y = ax^2
substitute A(-30, -10) in y = ax^2 we have
-10 = a(-30)^2
a = -10/(-30)^2
a = - 1/90
thus the equation is
y = -(1/90)x^2
y = - x^2/90
click here to see the graph of the equation