What is the directrix-3x^2+5x ?

The directrix-3x^2+5x is y= 13/6

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directrix-3x^2+5x

directrix

- 3 x^{2} + 5 x

y = \frac{13}{6}

Solution steps

Rewrite

y = - 3 x^{2} + 5 x

in the standard form

4 (- \frac{1}{12}) (y - \frac{25}{12}) = (x - \frac{5}{6})^{2}

(h, k) = (\frac{5}{6}, \frac{25}{12}), p = - \frac{1}{12}

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{5}{6}, \frac{25}{12})

y-coordinate

y = \frac{25}{12} - p

y = \frac{25}{12} - (- \frac{1}{12})

Refine

y = \frac{13}{6}

y = - x^{2} - 4 x - 3

y = 2 x^{2} + 3 π

x = (2 y - 1) (5 y - 6)

+ 2 (x + 1)^{2} - 3

x^{2} - 6 y = 0