What is the directrix y=(3x-7)^2 ?

The directrix y=(3x-7)^2 is y=-1/36

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directrix y=(3x-7)^2

directrix

y = (3 x - 7)^{2}

y = - \frac{1}{36}

Solution steps

Rewrite

y = (3 x - 7)^{2}

in the standard form:

4 \cdot \frac{1}{36} (y - 0) = (x - \frac{7}{3})^{2}

(h, k) = (\frac{7}{3}, 0), p = \frac{1}{36}

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{7}{3}, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{36}

Refine

y = - \frac{1}{36}

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

5 x^{2} - 15 x + 3

x^{2} + 10 x - 24

x (4 - x)

5 x^{2} - 3 x + 3