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

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

axis

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

x = \frac{1}{3}

Solution steps

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

Rewrite

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

in the standard form

4 \cdot \frac{1}{12} (y - \frac{5}{3}) = (x - \frac{1}{3})^{2}

Therefore parabola properties are:

(h, k) = (\frac{1}{3}, \frac{5}{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}

\frac{y - 2}{4} - \frac{x ^{2}}{9} = 1

y = 2 x^{2} + 24 x - 6

y = (2 x)^{2}

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

- y^{2} + x + 6 y - 14 = 0