What is the directrix-4x^2+2x+2 ?

The directrix-4x^2+2x+2 is y= 37/16

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directrix-4x^2+2x+2

directrix

- 4 x^{2} + 2 x + 2

y = \frac{37}{16}

Solution steps

Rewrite

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

in the standard form

4 (- \frac{1}{16}) (y - \frac{9}{4}) = (x - \frac{1}{4})^{2}

(h, k) = (\frac{1}{4}, \frac{9}{4}), p = - \frac{1}{16}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(\frac{1}{4}, \frac{9}{4})

y-coordinate

y = \frac{9}{4} - p

y = \frac{9}{4} - (- \frac{1}{16})

Refine

y = \frac{37}{16}

(y - 2)^{2} = 8 (x - 1)

y = 4 x + 4 x - 2 + x^{2} - 3

y = - 5 x^{2} + 118 x + 7

- x^{2}

x = - 8 y^{2}