Problema Solution
An arch in a memorial park, having a parabolic shape, has a height of 6 meters and a base width of 4 meters. Find an equation which models this shape.
Answer provided by our tutors
The vertex form of a parabola's equation is generally expressed as:
y = a(x-h)^2+k, where (h, k) is the vertex of the parabola, a is constant
in our case the vertex is (0, 6) (make a drawing) thus h = 0, k = 6
y = ax^2 + 6
since the parabola goes trough (-2, 0) and (2, 0) we have:
0 = a*2^2 + 6
a = - 6/4
a = - 3/2
a = -1.5
the equation that models this shape is:
y = -1.5x^2 + 6
click here to see the graph: