What is the axis of symmetry of the parabola?

Question

y = -x^2 + 2x

Answer 1

y = - ( x ² - 2 x )
y = - [ ( x ² - 2 x + 1) - 1 ]
y = - [ ( x - 1 ) ² - 1 ]
Axis of symmetry is x = 1

Answer 2

The axis of symmetry is an imaginary line that 'splits' the parabola in equal halves, such that one side is a mirror image of the other side. This (infinite) line of symmetry goes through the vertex and when dealing with functions is usually expressed as x= @#% at the line of symmetry.

There are many ways to find this line.
Concerning the equation you present above, the line of symmetry will have the numerical value of the x value at the vertex. One way to find the x value at the vertex is to use the formula x= -b/(2a)

You can see below where the (a), (b) and (c) come from in the equation:
y = ax^2 + bx + c

Your equation is:
y = -x^2 + 2x
you can see that the (a) is negative 1
the (b) is +2
and the (c) is 0 (but you don't need the (c) for the x value at the vertex.)
So then plug your (a) and (b) into x=-b/2a

x = -2/ (2(-1))
which simplifies down to
x = -2/-2
which is 1
x = 1
So the x value at the vertex is 1
And the axis of symmetry is described as:
x = 1
It is a vertical line of infinite length that goes through both the 1 (on the x axis) and the vertex.

Answer 3

This is a maximum
got to find the maximum point
completing square

y=-[(x-1)^2 -1]
Coordinate of max point: (1, -1)

therefore the axis of symmetry: x=1

Answer 4

The equation of the axis of symmetry is x=1. This can be found by using any method (calculus or otherwise) to find the coordinates of the turning point of the parabola.