What is the directrix-4x^2+6x-1 ?

The directrix-4x^2+6x-1 is y= 21/16

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directrix-4x^2+6x-1

directrix

- 4 x^{2} + 6 x - 1

y = \frac{21}{16}

Solution steps

Rewrite

y = - 4 x^{2} + 6 x - 1

in the standard form

4 (- \frac{1}{16}) (y - \frac{5}{4}) = (x - \frac{3}{4})^{2}

(h, k) = (\frac{3}{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{3}{4}, \frac{5}{4})

y-coordinate

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

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

Refine

y = \frac{21}{16}

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

y = - 4 x^{2} - 4

(x - 4)^{2} = - 8 (y + 3)

y^{2} + 33 = - 8 x - 23

x^{2} + 7 x + 12