What is the foci 2x^2+3x-20 ?

The foci 2x^2+3x-20 is (-3/4 ,-21)

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foci 2x^2+3x-20

foci

2 x^{2} + 3 x - 20

(- \frac{3}{4}, - 21)

Solution steps

Rewrite

y = 2 x^{2} + 3 x - 20

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{169}{8})) = (x - (- \frac{3}{4}))^{2}

(h, k) = (- \frac{3}{4}, - \frac{169}{8}), p = \frac{1}{8}

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

p

from the center

(- \frac{3}{4}, - \frac{169}{8})

along the y-axis

(- \frac{3}{4}, - \frac{169}{8} + p)

= (- \frac{3}{4}, - \frac{169}{8} + \frac{1}{8})

Refine

(- \frac{3}{4}, - 21)

x + 7 = \frac{1}{36} (y + 3)^{2}

2 y^{2} - 8 x = 0

y^{2} - 8 y + 4 x = 0

x^{2} + 20 y = 10

7 y^{2}