What is the directrix 5x(2x+4)-3x ?

The directrix 5x(2x+4)-3x is y=-29/4

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directrix 5x(2x+4)-3x

directrix

5 x (2 x + 4) - 3 x

y = - \frac{29}{4}

Solution steps

Rewrite

y = 5 x (2 x + 4) - 3 x

in the standard form

4 \cdot \frac{1}{40} (y - (- \frac{289}{40})) = (x - (- \frac{17}{20}))^{2}

(h, k) = (- \frac{17}{20}, - \frac{289}{40}), p = \frac{1}{40}

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{17}{20}, - \frac{289}{40})

y-coordinate

y = - \frac{289}{40} - p

y = - \frac{289}{40} - \frac{1}{40}

Refine

y = - \frac{29}{4}

x^{2} + 12 y = 0

3 x^{2} - 30 x + 77

y = 2 x^{2} + 28 x + 105

(x - 1)^{2} = - 2 y - 11

(x - 2)^{2} = 8 (y + 1)