Day ?? - Transformations of Quadratic Functions 2

Hey everyone, my name is Adam Lennox from Mr. P's Pre-Cal 30S class and I am going to explain what we did in class today. We learned how to complete the square with a coefficient in front of the x^2 value, which is also known as the "a" value.

First, I think you already know how to complete the square. If you do, that's great, but if you're still having trouble, I'll review how to complete the square without the coefficient or "a" value.

Example:

1) Substitute the y as 0, and take the "c" value which is +4, and move it to the other side. (This equation is in standard form)

2) Take the "b" value, which is -2, and divide that number by 2 and square it. (This formula isn't part of the equation)

3) Take that answer which is 1, and add it to both sides of the equation.

4) Now factor the side with the x^2, and add the terms on the opposite side.

5) Move the number on the side that the "y" value was on, which is -3, and move it to the other side.

And that's your answer in vertex form.

Next, we'll learn how to complete the square with a coefficient or an "a" value that is other than 1.

Example:

1) Substitute the y as 0, and move the "c" value which is -26, to the other side.

2) Now we factor the coefficient, or "a" value out of the equation, which is -1.

3) Take the "b" value which is now +10, divide it by 2 and square that number.

4) Take that answer which is +25 and add it to the side with brackets.

5) In order to add +25 to the opposite side, you have to multiply +25 with the number we factored out earlier which is -1. The number we add on the opposite side becomes -25.

6) Factor the terms in the bracket (the side with x^2), and add the terms on the opposite side. Remember to keep the coefficient (the negative 1)

7) Move the stand-alone number to the other side to complete your answer in vertex form.

When answering problems with a number other than one as the "a" value or coefficient, always remember to factor out the coefficient or "a" value so you can work with the equation. (Step 2 in the second example) Also, remember to multiply the coefficient value by the number you divided by 2 and squared before you add it to the opposite side. (Step 5 in the second example)

Hope I didn't confuse you guys, I like to do problems quickly and in a way that makes sense to me. Hey, at least I don't abbreviate my words! Have to go now, I smell pancit