What is the directrix-4x^2+8x+1 ?

The directrix-4x^2+8x+1 is y= 81/16

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directrix-4x^2+8x+1

directrix

- 4 x^{2} + 8 x + 1

y = \frac{81}{16}

Solution steps

Rewrite

y = - 4 x^{2} + 8 x + 1

in the standard form

4 (- \frac{1}{16}) (y - 5) = (x - 1)^{2}

(h, k) = (1, 5), 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

(1, 5)

y-coordinate

y = 5 - p

y = 5 - (- \frac{1}{16})

Refine

y = \frac{81}{16}

y = 2 x^{2} + 3 x + 1

x - 4 y^{2} = 0

x = (- y - 1) (y + 3)

y = 4 x^{2} - 8 x + 1

y = 24 x - 3 x^{2}