Question

what is the vertex form for :y=1/2x^2+5/3x

Answer 1

Complete the square:
\[\frac{1}{2}(x^2+\frac{10}{3}x)=\frac{1}{2}(x^2+\frac{10}{3}x+\frac{100}{36}-\frac{100}{36})=\frac{1}{2}((x+\frac{10}{6})^2-\frac{100}{36})\]\[=\frac{1}{2}(x+\frac{5}{3})^2-\frac{25}{18}\]
So the vertex is at x=-5/3