What is the foci 2x^2-36x+324 ?

The foci 2x^2-36x+324 is (9, 1297/8)

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foci 2x^2-36x+324

foci

2 x^{2} - 36 x + 324

(9, \frac{1297}{8})

Solution steps

Rewrite

y = 2 x^{2} - 36 x + 324

in the standard form

4 \cdot \frac{1}{8} (y - 162) = (x - 9)^{2}

(h, k) = (9, 162), p = \frac{1}{8}

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

p

from the center

(9, 162)

along the y-axis

(9, 162 + p)

= (9, 162 + \frac{1}{8})

Refine

(9, \frac{1297}{8})

y = a x^{2}

y = (2 X + 5) (3 X - 7)

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

y^{2} = 5 y + 7 x + 3

y = x^{2} - 5 x - 24