I think the problem with your answer is that you didn’t put it in a g(x) = [something] format. First, was the answer area presented to you with “g(x) = “ in front of it? If this was the case, the format of the answer you gave would imply g(x) = (x-2)^2 = 9/4, with two equal signs.

What you needed to do was to keep “g(x) =“ in your further calculations, instead of using equality to zero. So the Khan Academy method was the correct way to arrive at the answer.

Thank you for your feedback, Regina; but how does the format of the function affect the overall value? The way I understand it is that quadratic equations are equal to zero until a value is input for a given variable and the function notation is interchangeable with zero since it is merely a question of mathematical style and is not inherently integral in calculations of a function since it represents where the answer would go after evaluation.

Perhaps different teachers teach quadratic equations different ways, but the way I learned it, and the way I think Khan Academy teaches it is if there is a function indicator such as g(x) or a different variable such as y, that becomes part of the quadratic function and should not be thought of as zero. Any operations performed on the other side of the equals sign of the function indicator or 2nd variable needs to be done to that function indicator or 2nd variable.

So, dividing the whole original quadratic by 4 and totally discarding the 4 will not work if you want to leave g(x) untouched, which is desired for solving this problem. Instead, you need to factor out the 4 from the first two terms and keep the 4 outside parentheses, as the hints show.