Final answer:
To find the vertex of the quadratic function f(x) = x² + 4x + 3, you use the vertex formula (-b/(2a), f(-b/(2a))). The calculations give the vertex (-2, -1), which matches option B.
Step-by-step explanation:
To determine the vertex of the quadratic function f(x) = x² + 4x + 3, you can use the vertex formula which is (-b/(2a), f(-b/(2a))). The given function has the standard form ax² + bx + c where a = 1, b = 4, and c = 3. First, calculate the x-coordinate of the vertex using -b/(2a) which yields -4/(2×1) = -2. Then, substitute this x-coordinate back into the function to find the y-coordinate: f(-2) = (-2)² + 4(-2) + 3 = 4 - 8 + 3 = -1. Therefore, the vertex of the function is (-2, -1), which corresponds to option B).