What is the directrix y=2x^2+28x+105 ?

The directrix y=2x^2+28x+105 is y= 55/8

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directrix y=2x^2+28x+105

directrix

y = 2 x^{2} + 28 x + 105

y = \frac{55}{8}

Solution steps

Rewrite

y = 2 x^{2} + 28 x + 105

in the standard form

4 \cdot \frac{1}{8} (y - 7) = (x - (- 7))^{2}

(h, k) = (- 7, 7), p = \frac{1}{8}

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

(- 7, 7)

y-coordinate

y = 7 - p

y = 7 - \frac{1}{8}

Refine

y = \frac{55}{8}

(x - 1)^{2} = - 2 y - 11

(x - 2)^{2} = 8 (y + 1)

y^{2} = 24 x

y = - \frac{( x + 3 ) ^{2}}{20} + 1

x^{2} - 6 x + 10