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

The directrix ((4x+5)(2x+3))/2 is y=-1/8

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

directrix

\frac{( 4 x + 5 ) ( 2 x + 3 )}{2}

y = - \frac{1}{8}

Solution steps

Rewrite

y = \frac{( 4 x + 5 ) ( 2 x + 3 )}{2}

in the standard form

4 \cdot \frac{1}{16} (y - (- \frac{1}{16})) = (x - (- \frac{11}{8}))^{2}

(h, k) = (- \frac{11}{8}, - \frac{1}{16}), p = \frac{1}{16}

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{11}{8}, - \frac{1}{16})

y-coordinate

y = - \frac{1}{16} - p

y = - \frac{1}{16} - \frac{1}{16}

Refine

y = - \frac{1}{8}

y = 4 (x - 1)^{2} - 2

- 2 - x + x^{2}

(x - 1)^{2} - 2

y^{2} - 10 y + 4 x + 25 = 0

(x + 4)^{2} = - 6 (y - 3)

What is the directrix ((4x+5)(2x+3))/2 ?
The directrix ((4x+5)(2x+3))/2 is y=-1/8