Answer:
(1.25, 4.875)
Explanation:
To find the vertex we need to complete the square. In order to do this we need the coefficient of x² to be 1, so we take out a factor of 2 from the x² and x terms to get f(x) = 2(x² - 5/2x) + 8.
Now we complete the square as follows:
f(x) = 2[(x - 5/4)² - 25/16] + 8
f(x) = 2(x - 5/4)² - 25/8 + 8
f(x) = 2(x - 5/4)² + 39/8
Hence the vertex has coordinates (1.25, 4.875).