What is the directrix y=x^2-5x+3 ?

The directrix y=x^2-5x+3 is y=-7/2

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directrix y=x^2-5x+3

directrix

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

y = - \frac{7}{2}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{13}{4})) = (x - \frac{5}{2})^{2}

(h, k) = (\frac{5}{2}, - \frac{13}{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{13}{4})

y-coordinate

y = - \frac{13}{4} - p

y = - \frac{13}{4} - \frac{1}{4}

Refine

y = - \frac{7}{2}

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

(x - 6)^{2} = 8 (y - 2)

- x^{2} + 6 x + 19

- x^{2} + 5 x + 6

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