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

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axis y=2-x-2x^2

axis

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

x = - \frac{1}{4}

Solution steps

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

Rewrite

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

in the standard form

4 (- \frac{1}{8}) (y - \frac{17}{8}) = (x - (- \frac{1}{4}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{1}{4}, \frac{17}{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}

\frac{x ^{2}}{8} + \frac{y ^{2}}{3} = 1

f (x) = x^{2} + 6 x + 5

4 x^{2} - 12 y^{2} - 16 x - 72 y - 44 = 0

y^{2} = - 2 x

(x - 2)^{2} + (y - 3)^{2} = 64