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I have to solve this question:

The quadratic function f(x) = 2x² + ax - 1 in x satisfies f(-1)≥-3 ,f(2)≥3

Let us consider the minimum value m of f(x)

(1) m can be expressed in terms of a as: m = -A/B a² - C

(2) The range of the values of a such that f(x) satisfies condition 1 is -2≤a≤4

Where A, B and C are just the blanks to fill the answers, but what i don't understand is how to express m in terms of a

Science boy
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    Hint: f(x) is a upward-opening parabola with the $y$-value of its vertex being $m$ (it's probably a good idea to think through why this is the case). – Tony Ip May 05 '21 at 05:04
  • I see, it was very simple, i poorly interpreted the statement, i thought m was a variable with a minimum value in f(x), thank you very much! – Science boy May 05 '21 at 05:13

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