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

The solution to f(x)f(x)=3x^2-4x-3 is Hyperbola with (h,k)=(2/3 ,0),a=(sqrt(13))/3 ,b=sqrt(13/3)

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f(x)f(x)=3x^2-4x-3

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

(h, k) = (\frac{2}{3}, 0), a = \frac{13}{3}, b = \frac{13}{3}

Solution steps

yy = 3 x^{2} - 4 x - 3

Rewrite

yy - 3 x^{2} + 4 x + 3 = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{2}{3} ) ^{2}}{( \frac{13}{3} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{13}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{2}{3}, 0), a = \frac{13}{3}, b = \frac{13}{3}

- 81 x^{2} + 486 x + 64 y^{2} + 128 y + 4519 = 0

- 2 x^{2} + y^{2} + 20 x + 6 y - 45 = 0

\frac{y ^{2}}{80} - \frac{x ^{2}}{4} = 1

\frac{( y + 6 ) ^{2}}{25} - (x - 2)^{2} = 1

y^{2} \leq x^{2} - 1

What is f(x)f(x)=3x^2-4x-3 ?
The solution to f(x)f(x)=3x^2-4x-3 is Hyperbola with (h,k)=(2/3 ,0),a=(sqrt(13))/3 ,b=sqrt(13/3)