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

The directrix y=4x^2-2x+4 is y= 59/16

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

directrix

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

y = \frac{59}{16}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{16} (y - \frac{15}{4}) = (x - \frac{1}{4})^{2}

(h, k) = (\frac{1}{4}, \frac{15}{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{15}{4})

y-coordinate

y = \frac{15}{4} - p

y = \frac{15}{4} - \frac{1}{16}

Refine

y = \frac{59}{16}

x^{2} = 4 y + 8

\frac{9 x ^{2}}{2}

2 x^{2} + 8 x + 13

2 x^{2} - 4 x + 9

3 x^{2} - 31 x + 56 - (x - 8)