Question

What is the vertex of the function 2x2 + 16x + 21 = 0?

Answer 1

first coordinate of the vertex is found by the magic formula \(-\frac{b}{2a}\) in your case it is
\(-\frac{16}{2\times 2}=-4\)
second coordinate is found by replacing \(x\) by \(-4\) to see what you get

Answer 2

and not to be picky but
\[2x^2 + 16x + 21 = 0\] is not a function, it is a quadratic equation
\[f(x)=2x^2 + 16x + 21 \] is a function

Answer 3

and
\[f(-4)=2\times (-4)^2+16\times (-4)+21=-11\]so your vertex is \((-4,-11)\)