Question

Sara is completing the square to find the maximum or minimum value of the function f(x) = (2 - x) (5 + x). What is the first step that Sara must take? Does the function have a maximum or minimum value? What is that value?
A) multiply the binomials; maximum value;
49
4
B) multiply the binomials; minimum value;
49
4
C) set each factor equal to zero and solve for x; minimum value;
−2
5
D) set each factor equal to zero and solve for x; maximum value;
−7
2

Answer 1

Definitely multiply out the given factors:

f(x) = 10 + 2x - 5x - x^2, or  f(x) = -x^2 - 3x + 10
Find the derivative:  f '(x) = -2x - 3
Set the deriv. = to 0 and solve for x:  -2x = 3, and x = -3/2
This x = -3/2 is the x-coordinate of the max value.  The y-coord. is

f(-3/2) = (-3/2)^2 - 3(-3/2) + 10 = 21.25

I realize that this result does not agree with any of the four possible answers.  Please ensure that y ou have copied down this problem completely and correctly.