What is the axis y=(x^2+x)/2 ?

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axis y=(x^2+x)/2

axis

y = \frac{x ^{2} + x}{2}

x = - \frac{1}{2}

Solution steps

y = \frac{x ^{2} + x}{2}

Rewrite

y = \frac{x ^{2} + x}{2}

in the standard form

4 \cdot \frac{1}{2} (y - (- \frac{1}{8})) = (x - (- \frac{1}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{1}{2}, - \frac{1}{8}), p = \frac{1}{2}

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 = - \frac{1}{2}

y = 3 x^{2} - 8 x - 3

x = (3 y - 4) (4 y - 3) - 2 y

y = - 2 x^{2} - 16 x - 25

y = 2 x^{2} - x - 1

y = 6 - 2 x^{2}