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

The solution to f(x)f(x)=4x^2-x+2 is Hyperbola with (h,k)=(1/8 ,0),a=(sqrt(31))/4 ,b=(sqrt(31))/8

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

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

(h, k) = (\frac{1}{8}, 0), a = \frac{31}{4}, b = \frac{31}{8}

Solution steps

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

Rewrite

yy - 4 x^{2} + x - 2 = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{31}{4} ) ^{2}} - \frac{( x - \frac{1}{8} ) ^{2}}{( \frac{31}{8} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{8}, 0), a = \frac{31}{4}, b = \frac{31}{8}

\frac{( x - 2 ) ^{2}}{4} - (\frac{( y - 2 )}{5})^{2} = 1

\frac{x ^{2}}{5} - \frac{y ^{2}}{7} = 1

\frac{x ^{2}}{5 ^{2}} - \frac{y ^{2}}{3 ^{2}} = 1

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

- 4 x^{2} + 4 y^{2} - 24 x + 32 y = - 24

What is f(x)f(x)=4x^2-x+2 ?
The solution to f(x)f(x)=4x^2-x+2 is Hyperbola with (h,k)=(1/8 ,0),a=(sqrt(31))/4 ,b=(sqrt(31))/8