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The question refers to the equation of a parabola, that is, a quadratic equation of the form y = ax2 + bx + c.
Suppose x1 = -b/2a - z
and x2 = -b/2a + z for some real number z.
Then
y1 = a*(-b/2a - z)2 + b*(-b/2a - z) + c
= b2/4a + bz + az2 - b2/2a - bz + c
= b2/4a + az2 - b2/2a + c
and
y2 = (-b/2a + z)2 + b*(-b/2a + z) + c
= b2/4a - bz + az2 - b2/2a + bz + c
= b2/4a + az2 - b2/2a + c
So y1 = y2
thus, if x is the same distance (z) either side of -b/2a, then the corresponding y values are the same. And that, is what a line of symmetry means.
What else can I help you with?
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