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.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: