Find the minimum value of the function f(x)=x^(2)-14 x+41.3 to the nearest hundredth. Answer:

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Find the minimum value of the function  f(x)=x^(2)-14 x+41.3 to the nearest hundredth. Answer:

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Identify Coefficients: To find the minimum value of the quadratic function f(x) = x^2 - 14x + 41.3, we can complete the square or use the vertex formula for a parabola. The vertex form of a parabola is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Since the coefficient of x^2 is positive, the parabola opens upwards, and the vertex represents the minimum point.Calculate Vertex Coordinates: First, we identify the coefficients a, b, and c in the standard form of the quadratic function, which is f(x) = ax^2 + bx + c. Here, a = 1, b = -14, and c = 41.3.Find x-coordinate of Vertex: The x-coordinate of the vertex (h) can be found using the formula h = -b/(2a). Plugging in the values of a and b, we get h = -(-14)/(2*1) = 14/2 = 7.Find y-coordinate of Vertex: Now, we need to find the y-coordinate of the vertex (k), which is the value of the function at x = h. We substitute x = 7 into the function: f(7) = (7)^2 - 14*(7) + 41.3 = 49 - 98 + 41.3 = -49 + 41.3 = -7.7.Determine Vertex Minimum: The vertex of the parabola is at the point (7, -7.7). Since this is a parabola that opens upwards, the y-coordinate of the vertex, -7.7, represents the minimum value of the function.Round to Nearest Hundredth: We round the minimum value to the nearest hundredth, which gives us -7.70 as the final answer.

Find the minimum value of the function $f(x)=x^{2}-14 x+41.3$ to the nearest hundredth. $\newline$ Answer:

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Find the minimum value of the function f(x)=x2−14x+41.3 f(x)=x^{2}-14 x+41.3 f(x)=x2−14x+41.3 to the nearest hundredth.\newlineAnswer:

Find the minimum value of the function $f(x)=x^{2}-14 x+41.3$ to the nearest hundredth. $\newline$ Answer: