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

The directrix y=4x^2-8x+1 is y=-49/16

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directrix y=4x^2-8x+1

directrix

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

y = - \frac{49}{16}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{16} (y - (- 3)) = (x - 1)^{2}

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

y-coordinate

y = - 3 - p

y = - 3 - \frac{1}{16}

Refine

y = - \frac{49}{16}

y = 24 x - 3 x^{2}

x = - 5 y^{2}

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

2 (y - 1)^{2} - 4

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