What is the axis y=+2x^2-x-1 ?

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axis y=+2x^2-x-1

axis

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

x = \frac{1}{4}

Solution steps

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

Rewrite

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

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{9}{8})) = (x - \frac{1}{4})^{2}

Therefore parabola properties are:

(h, k) = (\frac{1}{4}, - \frac{9}{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}

(y - 0)^{2} = 4 x - 4

y = 12 x (x - 4)

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

y = 6 x^{2} - 29 x - 5

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