Hi

I have a question. Two points on a parabola is (-4,-1) and (-10,-1). what is the equation of the axis of symmetry?

how do you find it?

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If you analyse this you would see,

when x = -4, y = -1

and x = -10 also, y = -1

That means at -4 and -10, the parabola has same value and it is symmetrical in the middle point of [-4,-10] range.

The middle point is = (-4 -10)/2

= -7

Therefore the axis of symmetry is x = -7 or x+7 =0

If you look at this question carefully you'll realize that the y value of the two points are the same. This means that the two points make a horizontal line.
If the parabola was to have an axis of symmetry then it would mean that it must be right in the center of the two points.
So for the axis of symmetry i get x=-7.

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