What is the directrix 7x^2+70x+178 ?

The directrix 7x^2+70x+178 is y= 83/28

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directrix 7x^2+70x+178

directrix

7 x^{2} + 70 x + 178

y = \frac{83}{28}

Solution steps

Rewrite

y = 7 x^{2} + 70 x + 178

in the standard form

4 \cdot \frac{1}{28} (y - 3) = (x - (- 5))^{2}

(h, k) = (- 5, 3), p = \frac{1}{28}

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

(- 5, 3)

y-coordinate

y = 3 - p

y = 3 - \frac{1}{28}

Refine

y = \frac{83}{28}

x^{2} - 6 x - 28 y = - 93

x^{2} + 17 x + 16

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

y = x^{2} + x + 1

y = x^{2} + x + 3