What is the directrix y=5x^2+13x-6 ?

The directrix y=5x^2+13x-6 is y=-29/2

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directrix y=5x^2+13x-6

directrix

y = 5 x^{2} + 13 x - 6

y = - \frac{29}{2}

Solution steps

Rewrite

y = 5 x^{2} + 13 x - 6

in the standard form

4 \cdot \frac{1}{20} (y - (- \frac{289}{20})) = (x - (- \frac{13}{10}))^{2}

(h, k) = (- \frac{13}{10}, - \frac{289}{20}), p = \frac{1}{20}

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{13}{10}, - \frac{289}{20})

y-coordinate

y = - \frac{289}{20} - p

y = - \frac{289}{20} - \frac{1}{20}

Refine

y = - \frac{29}{2}

y = 3 x^{2} + 6 x - 12

(x - 5)^{2} = 20 (y - 5)

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

x = + \frac{17}{4} (y + 2)^{2}

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