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find all the possible x-coordinates of the vertex of parabol

Source: Albanian IMO 2011 TST

June 2, 2011
analytic geometryconicsparabolafunctionalgebra unsolvedalgebra

Problem Statement

The given parabola y=ax2+bx+cy=ax^2+bx+c doesn't intersect the XX-axis and passes from the points A(āˆ’2,1)A(-2,1) and B(2,9)B(2,9). Find all the possible values of the xx coordinates of the vertex of this parabola.
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