What is x^2-3x+k(x)-1=0 ?

The solution to x^2-3x+k(x)-1=0 is Parabola with (h,k)=(3/2 , 13/4),p=-1/4

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x^2-3x+k(x)-1=0

x^{2} - 3 x + k (x) - 1 = 0

(h, k) = (\frac{3}{2}, \frac{13}{4}), p = - \frac{1}{4}

Solution steps

x^{2} - 3 x + y - 1 = 0

Rewrite

x^{2} - 3 x + y - 1 = 0

in the standard form

4 (- \frac{1}{4}) (y - \frac{13}{4}) = (x - \frac{3}{2})^{2}

Therefore parabola properties are:

(h, k) = (\frac{3}{2}, \frac{13}{4}), p = - \frac{1}{4}

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

x = \frac{1}{12} y^{2}

4 x^{2} = 9 y

x^{2} - 8 x - 8 y = 0

y + 3 = 2 x + 5 x^{2}

What is x^2-3x+k(x)-1=0 ?
The solution to x^2-3x+k(x)-1=0 is Parabola with (h,k)=(3/2 , 13/4),p=-1/4