If the quadratic function f (x) = ax & # 178; + BX + C, f (- 1) = f (3) = 1, and the minimum value of F (x) is - 7, find the analytic expression of F (x) | Math enthusiast | Mathematical art

If the quadratic function f (x) = ax & # 178; + BX + C, f (- 1) = f (3) = 1, and the minimum value of F (x) is - 7, find the analytic expression of F (x)

f(-1)=f(3)=1
So the axis of symmetry is a straight line x = 1, that is - B / 2A = 1, that is 2A = - B
And when x = 1, f (1) = a + B + C = C-A = - 7, C = A-7
Because f (- 1) = A-B + C = 3A + C = 1
So we can get a = 2, B = - 4, C = - 5
So f (x) = 2x & # 178; - 4x-5

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