Math 2 Question

Question

Change the standard form equation y=x^2-6x+4 to vertex form by completing the square.

Please explain the problem!

Answer 1

In order to complete the square I would advise first seperating the x² and x term from the constant and leaving a space as shown:

y = x² -6x + 4

In order to complete the square you take half of the x term and square it. This will now be your constant needed to make a perfect square trinomial. For example with x² -6x you take half of -6 which is -3, then square it giving you 9. The perfect square trinomial would be:

x²-6x+9. Now you can write this as a squared binomial: (x-3)^2. (can check it by FOILing it out)

You get this by keeping the sign in front of the 6x, a negative, and taking half of 6 (which is 3).

Now back to the problem. Since you added 9 to the right-hand side to form the perfect square trinomial, you have to cancel it out on the same side

y = x² - 6x +9 +4 -9

We did this by also subtracting 9 on the right hand side. We have to do this because you cannot simply add numbers to an equation without changing its meaning. But a +9 and a -9 cancel out leaving the equation unchanged.

y = (x-3)² -5 now it is in vertex form