If f(x) = (x + 3)(x − 3), complete the square and determine the minimum or maximum value of the function. A) f(x) = (x + 0)2 − 9 and f(x) has a minimum value f(0) = −9. B) f(x) = (x + 0)2 − 9 and f(x) has a maximum value f(0) = −9. C) f(x) = (x+3)2 − 18 and f(x) has a maximum value f(−3) = −18. D) f(x) = (x+3)2 − 18 and f(x) has a minimum value f(−3) = −18.

  A)  f(x) = (x + 0)^2 − 9 and f(x) has a minimum value f(0) = −9

Step-by-step explanation:

The given factored form is the factorization of the difference of squares. When multiplied out, it becomes ...

  f(x) = x^2 -9

which can be written as ...

  f(x) = (x -0)^2 -9

Compared to vertex form ...

  f(x) = a(x -h)^2 +k

we find the vertex (h, k) to be (0, -9), and the scale factor a to be 1. The positive scale factor means the parabola opens upward, and the vertex represents a minimum.

  f(x) has a minimum at f(0) = -9.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.