Sam completed the square for the quadratic equation y=12x2−2x+3 in order to determine the minimum value of the equation, as shown. Step 1: y=12(x2−1x+32)
Step 2: y=12(x2−x+14−14+32)
Step 3: y=12((x−12)2−14+32)
Step 4: y=12((x−12)2+54)
Step 5: y=12(x−12)2+58
What mistake, if any, did Sam make?

a. In Step 2, she incorrectly added 14 and −14. She should have written 12(x2−x+12−12+6).
b. Sam did not make a mistake.
c. In Step 5, she incorrectly moved the fraction from the parentheses. She should have written 12(x−12)2+104.
d. In Step 1, she incorrectly factored out 12. She should have written y=12(x2−4x+6).

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.