What is the directrix-30x^2+28x-6 ?

The directrix-30x^2+28x-6 is y= 13/24

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directrix-30x^2+28x-6

directrix

- 30 x^{2} + 28 x - 6

y = \frac{13}{24}

Solution steps

Rewrite

y = - 30 x^{2} + 28 x - 6

in the standard form

4 (- \frac{1}{120}) (y - \frac{8}{15}) = (x - \frac{7}{15})^{2}

(h, k) = (\frac{7}{15}, \frac{8}{15}), p = - \frac{1}{120}

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{7}{15}, \frac{8}{15})

y-coordinate

y = \frac{8}{15} - p

y = \frac{8}{15} - (- \frac{1}{120})

Refine

y = \frac{13}{24}

y^{2} - 20 x = 0

x^{2} = 100 y

x = - \frac{1}{4} (y + 6)^{2} + 7

x^{2} + 2 y = 0

y = \frac{4 x ^{3} + 11 x ^{2} + 4 x + 21}{x + 3}