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Parabolas and completing the square

why the axis of symmetry is only the x co-ordinate of the turning point and not the y coordinate as well? how does the equation -b/2a relate to this?

Also, why is the x coordinate the opposite sign in the completing the square equation to the turning point value but not the y coordinate,

Reply 1

TeeEm

you need to expand on this perhaps with reference to a specific question

Reply 2

__Adam__

Original post by jm563

You need a line for an axis of symmetry, not a point. Try drawing a graph, you'll see that a line of symmetry goes up the middle of the parabola.

As for the -b/2a, look at translations, y = x^2 is symmetrical about the Y-axis (x=0), but y = (x-1)^2 is symmetrical about x=1 since the parabola is translated 1 to the right by replacing x with (x-1). You can generalise that to saying that y = (x-a)^2 is symmetrical about x=a since all you've done is shift the parabola to the right by a units.

Adding a constant to the function just moves the whole parabola up or down so that doesn't change the symmetry, so c is irrelevant here. Multiplying the entire function by a constant just stretches it vertically, so that doesn't change a vertical line of symmetry either. Try completing the square with y=ax^2+bx + c and see what you get.