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

The directrix-4x^2-2x+1 is y= 21/16

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directrix-4x^2-2x+1

directrix

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

y = \frac{21}{16}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (- \frac{1}{4}, \frac{5}{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{5}{4})

y-coordinate

y = \frac{5}{4} - p

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

Refine

y = \frac{21}{16}

(x + 5)^{2} = 12 (y - 2)

y^{2} + 4 x - 80 y + 20 = 0

- x^{2} - 4 x + 1

y - 7 = \frac{1}{24} (x + 4)^{2}

4 x^{2} - 24 x - 30