Question

Find the vertex of f(x)=3x2-24x+51

Answer 1

`\text{The vertex of}\ ax^2+bx+c:\\\\(h,\ k),\ \text{where}\ h=(-b)/(2a);\ k=f(h)=(-(-b^2-4ac))/(4a)`

`\text{We have:}\\f(x)=3x^2-24x+51\\\\a=3,\ b=-24,\ c=51\\\\h=(-(-24))/(2\cdot3)=(24)/(6)=4\\\\k=f(4)=3(4^2)-24(4)+51=3(16)-96+51=48-96+51=3`

`\text{Answer: the vertex is in}\ (4,\ 3)`