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

The directrix+(x-1)^2+2 is y= 7/4

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directrix+(x-1)^2+2

directrix

+ (x - 1)^{2} + 2

y = \frac{7}{4}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (1, 2), p = \frac{1}{4}

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, 2)

y-coordinate

y = 2 - p

y = 2 - \frac{1}{4}

Refine

y = \frac{7}{4}

3 - 4 x^{2}

2 y^{2} - 5 y + x - 4 = 0

x^{2} + 2 x - 8

x^{2} + 2 x - 1

y^{2} - 16 x = 0