Question

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?

Answer 1

In Step 1, she incorrectly factored out 1/2. She should have written y=1/2(x^2−4x+6).