Question

Find the vertex of the graph of the function.

f(x) = 3x^2 - 24x + 51

can someone help me understand vertex and how to solve for it please

Answer 1

\(\large { \displaystyle{\rm f}(x) = 3x^2 - 24x + 51}\)

\(\large { \displaystyle{\rm f}(x) = 3(x^2 - 8x) + 51}\)

\(\large { \displaystyle{\rm f}(x) = 3(x^2 - 8x\color{blue}{+16}\color{red}{-16}) + 51}\)

\(\large { \displaystyle{\rm f}(x) = 3(x^2 - 8x\color{blue}{+16})+3(\color{red}{-16}) + 51}\)

\(\large { \displaystyle{\rm f}(x) = 3(x-4)(x-4)-48 + 51}\)

\(\large { \displaystyle{\rm f}(x) = 3(x-4)^2+3}\)