What is the directrix 8-5x+x^2 ?

The directrix 8-5x+x^2 is y= 3/2

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directrix 8-5x+x^2

directrix

8 - 5 x + x^{2}

y = \frac{3}{2}

Solution steps

Rewrite

y = 8 - 5 x + x^{2}

in the standard form

4 \cdot \frac{1}{4} (y - \frac{7}{4}) = (x - \frac{5}{2})^{2}

(h, k) = (\frac{5}{2}, \frac{7}{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{5}{2}, \frac{7}{4})

y-coordinate

y = \frac{7}{4} - p

y = \frac{7}{4} - \frac{1}{4}

Refine

y = \frac{3}{2}

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

+ x^{2} + 4 x + 6

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

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

(y + 1)^{2} = 12 x