What is the standard form for y=7x^2+14x+4

That is standard form
standard form is y=ax²+bx+c where a,b, and c are constnats

that is standard form
if you wanted vertex form then
y=7(x²+2x)+4
y=7(x²+2x+1-1)+4
y=7((x+1)²-1)+4
y=7(x+1)²-7+4
y=7(x+1)²-3 which is vertex form

standard form is y=7x²+14x+4 or f(x)=7x²+14x+4