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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.

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sqdancefan

Answer:

  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.

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