What is the foci 2x^2-19x+9 ?

The foci 2x^2-19x+9 is (19/4 ,-36)

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foci 2x^2-19x+9

foci

2 x^{2} - 19 x + 9

(\frac{19}{4}, - 36)

Solution steps

Rewrite

y = 2 x^{2} - 19 x + 9

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{289}{8})) = (x - \frac{19}{4})^{2}

(h, k) = (\frac{19}{4}, - \frac{289}{8}), p = \frac{1}{8}

Parabola is symmetric around the y-axis and so the focus lies a distance

p

from the center

(\frac{19}{4}, - \frac{289}{8})

along the y-axis

(\frac{19}{4}, - \frac{289}{8} + p)

= (\frac{19}{4}, - \frac{289}{8} + \frac{1}{8})

Refine

(\frac{19}{4}, - 36)

(x + 5)^{2} = - 20 (y - 2)

x^{2} + 6 x - 8 y + 1 = 0

y = x^{2} + 1

290 (8 x + 0.5 x^{2} - 1.4)

y = - 3 x^{2} - 12 x - 9