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

The directrix 4+2x-x^2 is y= 21/4

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directrix 4+2x-x^2

directrix

y = \frac{21}{4}

Solution steps

Rewrite

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

in the standard form

4 (- \frac{1}{4}) (y - 5) = (x - 1)^{2}

(h, k) = (1, 5), 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, 5)

y-coordinate

y = 5 - p

y = 5 - (- \frac{1}{4})

Refine

y = \frac{21}{4}