Given: Prescription of the axis of symmetry: x = -1.5 Given two points: (-1,-12) and (-2,-12) The problem here is that the two given points have the same y-coordinate. With my normal method I therefore get a = 0 and I can’t get any further.
Answer
Dear, Lies
my previous answer contained an error, my apologies for that. Thanks to Hendrik Van Maldeghem (Ugent) for reporting it.
With the data you provide there is no unique solution. A parabola y = ax2 + bx + c with the vertical line x = -1.5 as axis of symmetry we can write in general as
y = A(x+1.5)2 + B with A different from 0, I forgot to add that B
however, if we fill in the two given points in this, we get twice the same equation in A and B. So one linear equation in two variables A and B:
0.25 A + B = -12
and this has infinitely many solutions.
Any parabola
y = A (x+1.5)2 -12 – 0.25 A (with A different from 0)
therefore meets the given requirements.
The system that was in the second part of the answer therefore has infinitely many solutions.
Answered by
prof.dr. Paul Hellings
Department of Mathematics, Fac. IIW, KU Leuven
Old Market 13 3000 Leuven
https://www.kuleuven.be/
.