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

The directrix y=4x^2-4x^1 is y=-17/16

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

directrix

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

y = - \frac{17}{16}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (\frac{1}{2}, - 1), 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}{2}, - 1)

y-coordinate

y = - 1 - p

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

Refine

y = - \frac{17}{16}

y = 3 x^{2} - x + 5

x = y^{2} - y - 42

x^{2} - 4 x - 8 y + 2 = 0

(3 x - 4) (4 x - 3) - 2 x

(x - 3)^{2} = - 12 y