find the equation of a parabola with vertex on the line y=2x, axis parallel to the x-axis and passing through (3/2, 1) and (3,4)

Answer 1

since the vertex is on the line y=2x, suppose it is at (h,2h). Then
x = a(y-2h)^2 + h
Now use the points to get
a(1-2h)^2 + h = 3/2
a(4-2h)^2 + h = 3
solve to get
x = -1/18 (y-7)^2 + 7/2
x = 1/2 (y-2)^2 + 1