What is (4p+12)^2-4*2(12p+q+12)>0 ?

The solution to (4p+12)^2-4*2(12p+q+12)>0 is Parabola with (h,k)=(0,6),p= 1/8

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(4p+12)^2-4*2(12p+q+12)>0

(4 p + 12)^{2} - 4 \cdot 2 (12 p + q + 12) > 0

(h, k) = (0, 6), p = \frac{1}{8}

Solution steps

(4 p + 12)^{2} - 4 \cdot 2 (12 p + q + 12) > 0

Rewrite

(4 p + 12)^{2} - 4 \cdot 2 (12 p + q + 12) > 0

in the standard form

4 \cdot \frac{1}{8} (q - 6) = (p - 0)^{2}

Therefore parabola properties are:

(h, k) = (0, 6), p = \frac{1}{8}

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

x^{2} + 5 y = 0

5 = y^{2} + x

x^{2} + 10 x + 25 = x + k (x)

9 x^{2} - 4 (y - 2) - 36 \geq 0

What is (4p+12)^2-4*2(12p+q+12)>0 ?
The solution to (4p+12)^2-4*2(12p+q+12)>0 is Parabola with (h,k)=(0,6),p= 1/8