Determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.
f(x)=(x−4)(x−8)
The given quadratic function is in the form f(x) = (x - 4)(x - 8).
To determine whether the function has a minimum or maximum, we can look at the leading coefficient of the quadratic term. In this case, the leading coefficient is positive (1), so the function will have a minimum point.
To find the minimum value of the function, we can either complete the square or use calculus. Since the function is in factored form, we can easily see that the x-coordinate of the minimum point is the average of the two zeros, which is x = (4 + 8)/2 = 6.
To find the corresponding y-value, we can substitute x = 6 back into the function:
f(6) = (6 - 4)(6 - 8) = (2)(-2) = -4
Therefore, the function has a minimum value of -4 at x = 6.