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

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

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directrix y=-3x^2+5x

directrix

y = - 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}

x^{2} + 16 x + 8

(x - 3)^{2} - 4

(y + 1.5)^{2} = 4 (x - 2)

x = (y - 3)^{2} + 2

14 x^{2}