What is the directrix y=(x-4)(x-7) ?

The directrix y=(x-4)(x-7) is y=-5/2

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directrix y=(x-4)(x-7)

directrix

y = (x - 4) (x - 7)

y = - \frac{5}{2}

Solution steps

Rewrite

y = (x - 4) (x - 7)

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{9}{4})) = (x - \frac{11}{2})^{2}

(h, k) = (\frac{11}{2}, - \frac{9}{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{11}{2}, - \frac{9}{4})

y-coordinate

y = - \frac{9}{4} - p

y = - \frac{9}{4} - \frac{1}{4}

Refine

y = - \frac{5}{2}

y = - 2 x^{2} + 6

y = - 2 x^{2} + 7

y = (7 x - 3)^{2}

+ 6 x^{2} - 54 x + 120

y = 9 x^{2} + 6 x + 1