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

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axis y=2x^2-x

axis

y = 2 x^{2} - x

x = \frac{1}{4}

Solution steps

y = 2 x^{2} - x

Rewrite

y = 2 x^{2} - x

in the standard form

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

Therefore parabola properties are:

(h, k) = (\frac{1}{4}, - \frac{1}{8}), p = \frac{1}{8}

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}{4}

(x + 3)^{2} = 4 (y - 1)

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

y = - x^{2} - 2 x + 7

y = 2 x^{2} - 7

(x + 1)^{2} = 12 y