What is the axis y=2x-x^2 ?

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axis y=2x-x^2

axis

y = 2 x - x^{2}

x = 1

Solution steps

y = 2 x - x^{2}

Rewrite

y = 2 x - x^{2}

in the standard form

4 (- \frac{1}{4}) (y - 1) = (x - 1)^{2}

Therefore parabola properties are:

(h, k) = (1, 1), p = - \frac{1}{4}

Parabola is of the form

4 p (y - k) = (x - h)^{2}

and is symmetric around the

y

-axis

Axis of symmetry is a line parallel to the

y

-axis which intersects the vertex:

x = 1

y = - x^{2} + 4 x - 4

y = x^{2} - 1

y = x^{2} - 12 x + 35

(x + 1)^{2} = (y + 4)

y = (2 x + 1)^{2}