Final answer:
The minimum value of the quadratic function f(x) = x^2 - 6x + 10 is calculated by finding the vertex of the parabola. The x-coordinate of the vertex is 3, and by plugging this value back into the function, we find the minimum value to be 1.
Step-by-step explanation:
To calculate the minimum value of the quadratic function f(x) = x2 − 6x + 10, we can complete the square or use the formula for the vertex of a parabola given by (-b/2a, f(-b/2a)) where f(x) = ax2 + bx + c.
Firstly, the coefficients of our function are a = 1, b = -6, and c = 10. To find the x-coordinate of the vertex, we use -b/2a:
x = −(−6)/(2*1) = 3
Now we can compute the y-coordinate, which is the minimum value of the function, by substituting this x-value back into the function:
f(3) = (3)2 − 6(3) + 10 = 9 − 18 + 10 = 1
Hence, the minimum value of the quadratic function is 1, which is not listed in the options given. Therefore, it looks like there might be a typo or oversight in the options provided.