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find the equation of a parabola with vertex on the line y=2x,
axis parallel to the y axis and passing through (3/2,1) & (3,4)
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Looking at the given points, I see that when we are moving from point (3/2,1) to point (3,4),
then x-coordinate doubles, while y-coordinate quadruples.
It leads me to the thought / (to the hypothesis) that the vertex is the point (0,0).
Indeed, then the parabola is y = = ,
and all the conditions of the problem are satisfied: the vertex lies on the line y = 2x
at (x,y) = (0,0), and the points do belong to this parabola, as you can easily check
by substituting the coordinates into the equation.
Solved.
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Notice that my solution is logically irreproachable.
An observation leads me to a hypothesis,
and then I check the hypothesis by direct calculations,
confirming that all the conditions of the problem are satisfied.