What is the directrix y=4x^2+23x-6 ?

The directrix y=4x^2+23x-6 is y=-313/8

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directrix y=4x^2+23x-6

directrix

y = 4 x^{2} + 23 x - 6

y = - \frac{313}{8}

Solution steps

Rewrite

y = 4 x^{2} + 23 x - 6

in the standard form

4 \cdot \frac{1}{16} (y - (- \frac{625}{16})) = (x - (- \frac{23}{8}))^{2}

(h, k) = (- \frac{23}{8}, - \frac{625}{16}), 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{23}{8}, - \frac{625}{16})

y-coordinate

y = - \frac{625}{16} - p

y = - \frac{625}{16} - \frac{1}{16}

Refine

y = - \frac{313}{8}

4 - X^{2}

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

\frac{1}{2} (x^{2} - 4 x + 2)

- x^{2} + 8 x - 7

y = x^{2} - 5 x + 4