Final answer:
To find the minimum value of the function f(x) = x² + 12.2x + 35.1, we can use the vertex form of a quadratic function. The vertex form is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Step-by-step explanation:
To find the minimum value of the function f(x) = x² + 12.2x + 35.1, we can use the vertex form of a quadratic function. The vertex form is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
In this case, a = 1, and the coefficient of x is positive. Therefore, the parabola opens upwards and the vertex represents the minimum value of the function.
To find the x-coordinate of the vertex, we can use the formula x = -b/(2a). Plugging in the values, we get x = -12.2/(2*1) = -6.1. Substituting this back into the original equation, we get f(-6.1) = (-6.1)² + 12.2(-6.1) + 35.1 = 19.81 - 74.42 + 35.1 = -19.51.
Therefore, the minimum value of the function is -19.51 to the nearest hundredth.