What is f(x)*f(x)=2x^2-x-10 ?

The solution to f(x)*f(x)=2x^2-x-10 is Hyperbola with (h,k)=(1/4 ,0),a= 9/4 ,b= 9/(2sqrt(2))

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f(x)*f(x)=2x^2-x-10

f (x) \cdot f (x) = 2 x^{2} - x - 10

(h, k) = (\frac{1}{4}, 0), a = \frac{9}{4}, b = \frac{9}{2 2}

Solution steps

yy = 2 x^{2} - x - 10

Rewrite

yy - 2 x^{2} + x + 10 = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{1}{4} ) ^{2}}{( \frac{9}{4} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{9}{2 2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{4}, 0), a = \frac{9}{4}, b = \frac{9}{2 2}

\frac{y ^{2}}{100} - \frac{( x - 2 ) ^{2}}{64} = 1

\frac{x ^{2}}{16} - \frac{( y + 6 ) ^{2}}{9} = 1

\frac{- ( x - 5 ) ^{2}}{16} + \frac{( y + 7 ) ^{2}}{9} = 1

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

y^{2} + C = (\frac{3 x ^{2}}{2} - 6 x + C)

What is f(x)*f(x)=2x^2-x-10 ?
The solution to f(x)*f(x)=2x^2-x-10 is Hyperbola with (h,k)=(1/4 ,0),a= 9/4 ,b= 9/(2sqrt(2))