What is the axis y=3x^2+2x+6 ?

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axis y=3x^2+2x+6

axis

y = 3 x^{2} + 2 x + 6

x = - \frac{1}{3}

Solution steps

y = 3 x^{2} + 2 x + 6

Rewrite

y = 3 x^{2} + 2 x + 6

in the standard form

4 \cdot \frac{1}{12} (y - \frac{17}{3}) = (x - (- \frac{1}{3}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{1}{3}, \frac{17}{3}), 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}{3}

x^{2} = - \frac{4}{5} (y - 2)

5 x - 6 - \frac{1}{2} y^{2} + 2 y^{2} = 0

y = x^{2} + 12 x + 6

y = - x^{2} + 120 x + 1300

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