Question

F(x)=x^(2)+2x+3 The range of f(x) is?

Answer 1

y ≥ 2 or [2, +∞)

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Given function:

• f(x) = x² + 2x + 3

This is a quadratic function in standard form.

Let's convert it into vertex form by completing the square:

• f(x) =
• x² + 2x + 3 =
• x² + 2x + 1 + 2 =
• (x + 1)² + 2

From the final expression we see it is a parabola that opens up (since leading coefficient is positive) and with minimum value at vertex, f(x) = 2, when x = - 1.

So its range is any value greater or equal to 2:

• Range: y ≥ 2 or [2, +∞)