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

The directrix (3x-4)(4x-3)-2x is y=-77/24

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

directrix

(3 x - 4) (4 x - 3) - 2 x

y = - \frac{77}{24}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{48} (y - (- \frac{51}{16})) = (x - \frac{9}{8})^{2}

(h, k) = (\frac{9}{8}, - \frac{51}{16}), p = \frac{1}{48}

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{9}{8}, - \frac{51}{16})

y-coordinate

y = - \frac{51}{16} - p

y = - \frac{51}{16} - \frac{1}{48}

Refine

y = - \frac{77}{24}

(x - 3)^{2} = - 12 y

x^{2} = 10 y

y = 6 x^{2} - 3 x 5

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

x^{2} - 6 x + 5 y = - 34

What is the directrix (3x-4)(4x-3)-2x ?
The directrix (3x-4)(4x-3)-2x is y=-77/24