What is the directrix y=(x+2)(x-3) ?

The directrix y=(x+2)(x-3) is y=-13/2

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directrix y=(x+2)(x-3)

directrix

y = (x + 2) (x - 3)

y = - \frac{13}{2}

Solution steps

Rewrite

y = (x + 2) (x - 3)

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{25}{4})) = (x - \frac{1}{2})^{2}

(h, k) = (\frac{1}{2}, - \frac{25}{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{1}{2}, - \frac{25}{4})

y-coordinate

y = - \frac{25}{4} - p

y = - \frac{25}{4} - \frac{1}{4}

Refine

y = - \frac{13}{2}

y = + 3 x^{2} + 24 x - 51

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

x^{2} + 5 x - 14

(x - 2) = 3 (y - 5)^{2}

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