What is the directrix y=x^2-4x+9 ?

The directrix y=x^2-4x+9 is y= 19/4

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directrix y=x^2-4x+9

directrix

y = x^{2} - 4 x + 9

y = \frac{19}{4}

Solution steps

Rewrite

y = x^{2} - 4 x + 9

in the standard form

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

(h, k) = (2, 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

(2, 5)

y-coordinate

y = 5 - p

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

Refine

y = \frac{19}{4}

(3 x - 2) (2 x + 1)

8 - 5 x + x^{2}

x^{2} - 4 x - 5 y + 7 = 0

+ x^{2} + 4 x + 6

\frac{( x - 3 ) ^{2}}{8} + 5