[tex]y= \frac{2}{5}x^2 +\frac{1 }{2}x+2 \\ \\ form\ of \ the \ standard \ equation:\\\\ y = ax^2 + bx + c\\\\ vertex (h, k)[/tex]
[tex]h=\frac{-b}{2a}\\\\k=g(h) \\ \\a=\frac{2}{5}, \ \ \ b=\frac{1}{2}\\\\h=\frac{-\frac{1}{2}}{2\cdot \frac{2}{5}}=-\frac{1}{2}:\frac{4}{5}=-\frac{1}{2} \cdot \frac{5}{4}=-\frac{5}{8}\\\\[/tex]
[tex]k=y(-\frac{5}{8})= \frac{2}{5} \cdot (-\frac{5}{8})^2 +\frac{1 }{2} \cdot (-\frac{5}{8})+2= \frac{2}{5} \cdot \frac{25}{64} -\frac{5}{16} +2 =\\\\= \frac{ 5}{32} -\frac{5}{16} +2 = \frac{ 5}{32} -\frac{10}{32} + \frac{64}{32} =\frac{(5-10+64)}{32}=\frac{59}{32}\\\\Answer: \ Vertex : (-\frac{5}{8};\frac{59}{32})[/tex]
