What is y^2+5y+25/4 =8x-13+25/4 ?

The solution to y^2+5y+25/4 =8x-13+25/4 is Parabola with (h,k)=(27/32 ,-5/2),p=2

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y^2+5y+25/4 =8x-13+25/4

y^{2} + 5 y + \frac{25}{4} = 8 x - 13 + \frac{25}{4}

(h, k) = (\frac{27}{32}, - \frac{5}{2}), p = 2

Solution steps

y^{2} + 5 y + \frac{25}{4} = 8 x - 13 + \frac{25}{4}

Rewrite

y^{2} + 5 y + \frac{25}{4} = 8 x - 13 + \frac{25}{4}

in the standard form

4 \cdot 2 (x - \frac{27}{32}) = (y - (- \frac{5}{2}))^{2}

Therefore parabola properties are:

(h, k) = (\frac{27}{32}, - \frac{5}{2}), p = 2

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

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

y \geq - 2 x^{2} - 2

y \geq - x^{2} + 4 x - 6

x^{2} \geq 2 y

What is y^2+5y+25/4 =8x-13+25/4 ?
The solution to y^2+5y+25/4 =8x-13+25/4 is Parabola with (h,k)=(27/32 ,-5/2),p=2