What is the directrix y=1-x-x^2 ?

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

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directrix y=1-x-x^2

directrix

y = 1 - x - x^{2}

y = \frac{3}{2}

Solution steps

Rewrite

y = 1 - x - x^{2}

in the standard form

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

(h, k) = (- \frac{1}{2}, \frac{5}{4}), 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

(- \frac{1}{2}, \frac{5}{4})

y-coordinate

y = \frac{5}{4} - p

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

Refine

y = \frac{3}{2}

- \frac{( x + 3 ) ^{2}}{20} + 1

y = \frac{- 3 x ^{2} - 2 x + 6}{5}

X^{2}

x^{2} + 2 x + 3

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