What is the directrix 2x^2-4x+15 ?

The directrix 2x^2-4x+15 is y= 103/8

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directrix 2x^2-4x+15

directrix

2 x^{2} - 4 x + 15

y = \frac{103}{8}

Solution steps

Rewrite

y = 2 x^{2} - 4 x + 15

in the standard form

4 \cdot \frac{1}{8} (y - 13) = (x - 1)^{2}

(h, k) = (1, 13), 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

(1, 13)

y-coordinate

y = 13 - p

y = 13 - \frac{1}{8}

Refine

y = \frac{103}{8}

y = - \frac{1}{8} x^{2}

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

x^{2} = - 20 y

y = 3 x^{2} - 2 x - 6

t^{2} + 2 t - 48