What is the directrix 2x^2-7x+15 ?

The directrix 2x^2-7x+15 is y= 35/4

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directrix 2x^2-7x+15

directrix

2 x^{2} - 7 x + 15

y = \frac{35}{4}

Solution steps

Rewrite

y = 2 x^{2} - 7 x + 15

in the standard form

4 \cdot \frac{1}{8} (y - \frac{71}{8}) = (x - \frac{7}{4})^{2}

(h, k) = (\frac{7}{4}, \frac{71}{8}), 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

(\frac{7}{4}, \frac{71}{8})

y-coordinate

y = \frac{71}{8} - p

y = \frac{71}{8} - \frac{1}{8}

Refine

y = \frac{35}{4}

3 x^{2} - 12 x + 5

18 x^{2} - 6 x + 4

x^{2} - 4 x - y + 3 = 0

y = - 3 (x - 2) (x + 5)

5 x^{2} + 4 x - 9