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

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axis x=y-y^2

axis

x = y - y^{2}

y = \frac{1}{2}

Solution steps

x = y - y^{2}

Rewrite

x = y - y^{2}

in the standard form

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

Therefore parabola properties are:

(h, k) = (\frac{1}{4}, \frac{1}{2}), p = - \frac{1}{4}

Parabola is of the form

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

and is symmetric around the

x

-axis

Axis of symmetry is a line parallel to the

x

-axis which intersects the vertex:

y = \frac{1}{2}

y = x^{2} - 5 x

y = 600 - 10 x + 0.25 x^{2}

y = - 0.00004 x^{2} - 0.00105 x + 1.055

(x + 3)^{2} = 5 y - 8

x = \frac{( y - 3 ) ^{2}}{8} + 5