ax2 + bx + c = y How is "a" connected to the 2nd difference sequence?

In the sequence given below,.
[tex]-4x^2+30x+74=y[/tex]In relation to the general equation of a quadratic formula,
[tex]ax^2+bx+c=y[/tex]Where, a, is the cofficient of x^2,
b is the coeffient of x and,
c is constant,
Relating the two equations,
[tex]\begin{gathered} a=-4 \\ b=30\text{ and,} \\ c=74 \\ ax^2+bx+c=y \\ -4x^2+30x+74=y^{}^{} \end{gathered}[/tex]Hence, a = -4 in the sequence.