What is the directrix 2x^2-x+1 ?

The directrix 2x^2-x+1 is y= 3/4

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directrix 2x^2-x+1

directrix

2 x^{2} - x + 1

y = \frac{3}{4}

Solution steps

Rewrite

y = 2 x^{2} - x + 1

in the standard form

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

(h, k) = (\frac{1}{4}, \frac{7}{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{1}{4}, \frac{7}{8})

y-coordinate

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

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

Refine

y = \frac{3}{4}

y^{2} = x

20 x = y^{2}

(x + 5)^{2} = 3 (y - 3)

12 (x - 2) = (y + 2)^{2}

y = - 5 x^{2}