What is the directrix 100+6x^2-8x ?

The directrix 100+6x^2-8x is y= 2335/24

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directrix 100+6x^2-8x

directrix

100 + 6 x^{2} - 8 x

y = \frac{2335}{24}

Solution steps

Rewrite

y = 100 + 6 x^{2} - 8 x

in the standard form

4 \cdot \frac{1}{24} (y - \frac{292}{3}) = (x - \frac{2}{3})^{2}

(h, k) = (\frac{2}{3}, \frac{292}{3}), 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{2}{3}, \frac{292}{3})

y-coordinate

y = \frac{292}{3} - p

y = \frac{292}{3} - \frac{1}{24}

Refine

y = \frac{2335}{24}

x^{2} - 6 x + 5

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

- x^{2} - 2 x - 3

- x^{2} - 2 x - 1

y + 3 x^{2} = 0