What is [f(x)]^2=4x^2-x+3 ?

The solution to [f(x)]^2=4x^2-x+3 is Hyperbola with (h,k)=(1/8 ,0),a=(sqrt(47))/4 ,b=(sqrt(47))/8

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[f(x)]^2=4x^2-x+3

[f (x)]^{2} = 4 x^{2} - x + 3

(h, k) = (\frac{1}{8}, 0), a = \frac{47}{4}, b = \frac{47}{8}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{47}{4} ) ^{2}} - \frac{( x - \frac{1}{8} ) ^{2}}{( \frac{47}{8} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{8}, 0), a = \frac{47}{4}, b = \frac{47}{8}

2 x^{2} - 3 y^{2} - 6 = 0

\frac{( x - 6 ) ^{2}}{48} - (y - 2)^{2} = 1

1680 = \frac{a}{b} a - b

a^{2} + 9 = c^{2}

3 x^{2} - 2 y^{2} + 4 y - 26 = 0

What is [f(x)]^2=4x^2-x+3 ?
The solution to [f(x)]^2=4x^2-x+3 is Hyperbola with (h,k)=(1/8 ,0),a=(sqrt(47))/4 ,b=(sqrt(47))/8