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Parabolas and completing the square watch

1. 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,
2. you need to expand on this perhaps with reference to a specific question
3. (Original post by jm563)
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,
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.
4. (Original post by TeeEm)
you need to expand on this perhaps with reference to a specific question
so for attached image, why is the equation y=(x-2)^2 +4 instead of y=(x+2)^2 +4
Attached Images

5. (Original post by jm563)
so for attached image, why is the equation y=(x-2)^2 +4 instead of y=(x+2)^2 +4
they are both wrong
6. (Original post by TeeEm)
they are both wrong
sorry it would be y=(x-2)^2 -4
7. (Original post by jm563)
sorry it would be y=(x-2)^2 -4
x2 to (x-2)2 represents a translation 2 units to the right
8. From the stationary point, you know that (2+a)^2 +b =-4 and that dy/dx =0 when x=2 using this you can find a and b

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Updated: February 28, 2016
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