Question

If 𝒇(𝒙)=𝒙𝟐+𝟒𝒙+𝟕find:a)The smallest possible value of 𝒇(𝒙)

Answer 1

so like a first step do you know this :
- If the parabola opens upward, you will be finding its minimum value. If the parabola opens downward, you will find its maximum value. ?

Answer 2

and the same : A quadratic function results in the graph of a parabola. The parabola either opens upward or downward. If ,,a", the coefficient of the x^{2} term, is positive, then the parabola opens upward. If ,,a" is negative, then the parabola opens downward

Answer 3

or have you heard about this ?
The maximum or minimum of a quadratic function occurs at
x=−b/2a
- If a is negative, the maximum value of the function is f(−b/2a)
- If a is positive, the minimum value of the function is f(−b/2a)