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

The solution to [f(x)]^2=4x^2-x+4 is Hyperbola with (h,k)=(1/8 ,0),a=(3sqrt(7))/4 ,b=(3sqrt(7))/8

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

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

(h, k) = (\frac{1}{8}, 0), a = \frac{3 7}{4}, b = \frac{3 7}{8}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{3 7}{4} ) ^{2}} - \frac{( x - \frac{1}{8} ) ^{2}}{( \frac{3 7}{8} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{8}, 0), a = \frac{3 7}{4}, b = \frac{3 7}{8}

\frac{x ^{2}}{81} - \frac{y ^{2}}{144} = 1

x^{2} - y^{2} - 11 = 5

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

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

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

What is [f(x)]^2=4x^2-x+4 ?
The solution to [f(x)]^2=4x^2-x+4 is Hyperbola with (h,k)=(1/8 ,0),a=(3sqrt(7))/4 ,b=(3sqrt(7))/8