What is the directrix x^2-6x+10 ?

The directrix x^2-6x+10 is y= 3/4

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directrix x^2-6x+10

directrix

x^{2} - 6 x + 10

y = \frac{3}{4}

Solution steps

Rewrite

y = x^{2} - 6 x + 10

in the standard form

4 \cdot \frac{1}{4} (y - 1) = (x - 3)^{2}

(h, k) = (3, 1), 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

(3, 1)

y-coordinate

y = 1 - p

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

Refine

y = \frac{3}{4}

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

y = 2 x^{2} - 3 x

2 x^{2} - 2

2 x^{2} + 3

x^{2} + x + 1