What is the foci-30x^2+28x-6 ?

The foci-30x^2+28x-6 is (7/15 , 21/40)

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foci-30x^2+28x-6

foci

- 30 x^{2} + 28 x - 6

(\frac{7}{15}, \frac{21}{40})

Solution steps

Rewrite

y = - 30 x^{2} + 28 x - 6

in the standard form

4 (- \frac{1}{120}) (y - \frac{8}{15}) = (x - \frac{7}{15})^{2}

(h, k) = (\frac{7}{15}, \frac{8}{15}), p = - \frac{1}{120}

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

p

from the center

(\frac{7}{15}, \frac{8}{15})

along the y-axis

(\frac{7}{15}, \frac{8}{15} + p)

= (\frac{7}{15}, \frac{8}{15} + (- \frac{1}{120}))

Refine

(\frac{7}{15}, \frac{21}{40})

(x + 5)^{2} + 4

y = - 8 x^{2}

y^{2} = \frac{16}{3} x

\frac{( x - 3 ) ^{2}}{8} + 5

(x + 5)^{2} + 3