What is the directrix y=4x^2-24x+31 ?

The directrix y=4x^2-24x+31 is y=-81/16

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directrix y=4x^2-24x+31

directrix

y = 4 x^{2} - 24 x + 31

y = - \frac{81}{16}

Solution steps

Rewrite

y = 4 x^{2} - 24 x + 31

in the standard form

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

(h, k) = (3, - 5), 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

(3, - 5)

y-coordinate

y = - 5 - p

y = - 5 - \frac{1}{16}

Refine

y = - \frac{81}{16}

y = - x^{2} + 4 x

y^{2} + 4 x - 14 y = - 53

y = 6 x^{2} + 12 x

y = - 4 (x - 2)^{2} + 16

4 X^{2} + 12 X + 9