What is the directrix ((x-5)(x-10))/(50) ?

The directrix ((x-5)(x-10))/(50) is y=-101/8

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directrix ((x-5)(x-10))/(50)

directrix

\frac{( x - 5 ) ( x - 10 )}{50}

y = - \frac{101}{8}

Solution steps

Rewrite

y = \frac{( x - 5 ) ( x - 10 )}{50}

in the standard form

4 \cdot \frac{25}{2} (y - (- \frac{1}{8})) = (x - \frac{15}{2})^{2}

(h, k) = (\frac{15}{2}, - \frac{1}{8}), p = \frac{25}{2}

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{15}{2}, - \frac{1}{8})

y-coordinate

y = - \frac{1}{8} - p

y = - \frac{1}{8} - \frac{25}{2}

Refine

y = - \frac{101}{8}

2 x^{2} - 12 x + 14 - 14 y = 0

(4 - x)^{2}

y = 7 x^{2}

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

y = (6 x - 1) (3 x - 2)

What is the directrix ((x-5)(x-10))/(50) ?
The directrix ((x-5)(x-10))/(50) is y=-101/8