What is the foci (4x^3-7x^2-11x+5)/(4x+5) ?

The foci (4x^3-7x^2-11x+5)/(4x+5) is (3/2 ,-1)

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foci (4x^3-7x^2-11x+5)/(4x+5)

foci

\frac{4 x ^{3} - 7 x ^{2} - 11 x + 5}{4 x + 5}

(\frac{3}{2}, - 1)

Solution steps

Rewrite

y = \frac{4 x ^{3} - 7 x ^{2} - 11 x + 5}{4 x + 5}

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{5}{4})) = (x - \frac{3}{2})^{2}

(h, k) = (\frac{3}{2}, - \frac{5}{4}), p = \frac{1}{4}

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

p

from the center

(\frac{3}{2}, - \frac{5}{4})

along the y-axis

(\frac{3}{2}, - \frac{5}{4} + p)

= (\frac{3}{2}, - \frac{5}{4} + \frac{1}{4})

Refine

(\frac{3}{2}, - 1)

y = 3 x^{2} - 5 x

2 x^{2} - 12 x + 14 - 14 y = 0

x = - 3 y^{2} + 5

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

6 x^{2} - 24 x - 30

What is the foci (4x^3-7x^2-11x+5)/(4x+5) ?
The foci (4x^3-7x^2-11x+5)/(4x+5) is (3/2 ,-1)