Question

What is the vertex of the function f(x) = 1/2x^2 + 3x + 3/2 ?

Answer 1

`\boxed{\bold{f(x)=\frac12(x-3)^2+15}}`

Explanation:

`f(x)=a(x-h)^2+k\qquad\qquad h=(-b)/(2a)\,,\ \ k=f(h)\\\\\\f(x)=\frac12x^2+3x+\frac32\quad\implies\quad a=\frac12\,,\ b=3\\\\h=(-3)/(2\cdor(-\frac12))=(-3)/(-1)=3\\\\h=f(3)=\frac12(3)^2+3\cdot3+\frac32=4\frac12+9+\frac32=15\\\\\\ \underline{f(x)=\frac12(x-3)^2+15}`