What is the axis y=3x^2-x-2 ?

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axis y=3x^2-x-2

axis

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

x = \frac{1}{6}

Solution steps

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

Rewrite

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

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{25}{12})) = (x - \frac{1}{6})^{2}

Therefore parabola properties are:

(h, k) = (\frac{1}{6}, - \frac{25}{12}), p = \frac{1}{12}

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}{6}

y = \frac{6 x}{7} \frac{4 x}{3}

y = + 6 x^{2} - 54 x + 120

y = 9 x^{2}

x^{2} = 3 y

9 y^{2} - 6 y - 9 - x = 0