What is 1/4 y+2x^2+3x=9 ?

The solution to 1/4 y+2x^2+3x=9 is Parabola with (h,k)=(-3/4 , 81/2),p=-1/32

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1/4 y+2x^2+3x=9

\frac{1}{4} y + 2 x^{2} + 3 x = 9

(h, k) = (- \frac{3}{4}, \frac{81}{2}), p = - \frac{1}{32}

Solution steps

\frac{1}{4} y + 2 x^{2} + 3 x = 9

Rewrite

\frac{1}{4} y + 2 x^{2} + 3 x = 9

in the standard form

4 (- \frac{1}{32}) (y - \frac{81}{2}) = (x - (- \frac{3}{4}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{3}{4}, \frac{81}{2}), p = - \frac{1}{32}

(x - 3)^{2} = 11 (y - 4)

x^{2} + 4 x - 4 y + 8 = 0

9 x^{2} - 12 x + 8 y - 32 = 0

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

x^{2} + 9 y = 6

What is 1/4 y+2x^2+3x=9 ?
The solution to 1/4 y+2x^2+3x=9 is Parabola with (h,k)=(-3/4 , 81/2),p=-1/32