What is f(x)f(x)=x^2-x+1 ?

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

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f(x)f(x)=x^2-x+1

f (x) f (x) = x^{2} - x + 1

(h, k) = (\frac{1}{2}, 0), a = \frac{3}{2}, b = \frac{3}{2}

Solution steps

yy = x^{2} - x + 1

Rewrite

yy - x^{2} + x - 1 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, 0), a = \frac{3}{2}, b = \frac{3}{2}

- 9 x^{2} + 4 y^{2} - 108 x + 32 y - 296 = 0

\frac{( x - 1 ) ^{2}}{9} - \frac{y ^{2}}{5} = 100

x^{2} = 2 y^{2} - 2 \cdot 0.01

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

\frac{y ^{2}}{4} - \frac{x ^{2}}{9} = 1 y

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