Question

Complete the square to find the vertex form of the parabola. f(x)=x^2-4x+3

Answer 1

So when we complete the square, we want to first deal with only the x-terms and secondly, make sure the coefficient of the x^2 term is one. It already is one, so that makes our life a little easier. So the purpose of completing the square is to change the form othe equation. This is done by finding a number such that the quadratic perfect square. So here's the set-up:

(x^2 - 4x + ___) + 3 = + ____

We willl find some number that will get added inside of the parenthesis as well as on the other side of the equation. So the way we find this number is we take the coefficient of the x-term, namely 4, then we half it and square it. I guess you can think of it as a quick phrase "half it and square it". SO taking half of -4 gives us -2. Squaring that gives us 4. So this 4 is the number we add into the two blanks I added:

(x^2 - 4x + 4) + 3 = 4. Now, the quadratic inside of the parenthesis is a perfect square. This is rewritten by taking half of the coefficient of the x-term, the -4 here, and pairing it with x. This means we have (x-2). This is then squared, (x-2)^2. So the final rewrite is (x-2)^2 + 3 = 4. From here you can get the vertex?