What is the foci 4x^2-4x+3 ?

The foci 4x^2-4x+3 is (1/2 , 33/16)

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foci 4x^2-4x+3

foci

4 x^{2} - 4 x + 3

(\frac{1}{2}, \frac{33}{16})

Solution steps

Rewrite

y = 4 x^{2} - 4 x + 3

in the standard form

4 \cdot \frac{1}{16} (y - 2) = (x - \frac{1}{2})^{2}

(h, k) = (\frac{1}{2}, 2), p = \frac{1}{16}

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

p

from the center

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

along the y-axis

(\frac{1}{2}, 2 + p)

= (\frac{1}{2}, 2 + \frac{1}{16})

Refine

(\frac{1}{2}, \frac{33}{16})

- 2 x^{2} + 4 x - 6

y^{2} - 4 y - 8 x + 44 = 0

y^{2} + 8 y - 12 x - 20 = 0

- 9 x^{2}

- 2 x^{2} + 12 x - 10