What is the axis y=2x^2-4x-1 ?

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axis y=2x^2-4x-1

axis

y = 2 x^{2} - 4 x - 1

x = 1

Solution steps

y = 2 x^{2} - 4 x - 1

Rewrite

y = 2 x^{2} - 4 x - 1

in the standard form

4 \cdot \frac{1}{8} (y - (- 3)) = (x - 1)^{2}

Therefore parabola properties are:

(h, k) = (1, - 3), 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 = 1

x^{2} = 20 y

2 y^{2} - 16 x = 0

y = + 2 - x^{2}

y = 2 x^{2} + 20 x + 48

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