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If you have done Calculus, you get a Stationary Point at dy/dx = 0 i.e. 10x + 20 = 0, so at x = -2, and y = 5*2^2 + 20*-2 + 17 = 20 - 40 + 17 = -3. If you have not done Calculus, find the vertex by Completing the Square i..e. F(x) = 5(x^2 + 4x) +17 = 5(x^2 + 4x + 4) + 17 - 20 = 5(x+2)^2 - 3. Since the bracket is squared it can never be negative so its minimum value is 0, at x = -2 i.e. the minimum value is - 3