What is the directrix (3x-2)(2x+1) ?

The directrix (3x-2)(2x+1) is y=-25/12

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directrix (3x-2)(2x+1)

directrix

(3 x - 2) (2 x + 1)

y = - \frac{25}{12}

Solution steps

Rewrite

y = (3 x - 2) (2 x + 1)

in the standard form

4 \cdot \frac{1}{24} (y - (- \frac{49}{24})) = (x - \frac{1}{12})^{2}

(h, k) = (\frac{1}{12}, - \frac{49}{24}), p = \frac{1}{24}

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{1}{12}, - \frac{49}{24})

y-coordinate

y = - \frac{49}{24} - p

y = - \frac{49}{24} - \frac{1}{24}

Refine

y = - \frac{25}{12}

8 - 5 x + x^{2}

x^{2} - 4 x - 5 y + 7 = 0

+ x^{2} + 4 x + 6

\frac{( x - 3 ) ^{2}}{8} + 5

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