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Because it is in the form of
Ax^2 + Bx + C
it is a "quadratic" -- a parabola
By looking at the coefficient associated with the x^2 term we can tell whether it opens upwards (positive coefficient) or downwards (negative coefficient). It is positive so it opens upwards.
Finding the vertex give you the minimum.
it is minimum when
x = -b/(2a) = -17/(2*5) = -17/10 = -1.7
Plug it back into the original equation to find the minimum: