How to convert a function from y=ax2+bx+c to y=a(x - h)2 +k by COMPLETING SQUARES

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Example: y= x2 -8x+7=0

1.- First, you need to make f(x) (the function/y) equal to 0.

Then, pass the “=0” to the right to make the clearing easier.

x2 -8x+7=0

2.- As a second step, you need to pass the constant term to the other side. (The one without variable)

x2 -8x=-7

3.- Now, we are going to COMPLETE SQUARES.

For this, you need to divide the second term over 2 and elevate it to the square. Afterwards, you have to add the result on both sides of the function.

x2 -8x+ (-8/2) 2 =-7+ (-8/2) 2

x2 -8x+ (64/4)  =-7+(64/4)

x2 -8x+ (16)  =-7+(16)

4.- When having this result, you will need to convert it to (a+b) 2

For doing this, you get the square root of the third term and add the result to the square root of the first term with the sign of the second term. Then, you need to elevate everything to the square.

(x-4) 2 =-7+(16)

(x-4) 2 =9

5.- Equal everything to 0 passing the constant number to the left of the equal sign.

(x-4) 2 -9=0

6.- Make 0 “f(x)” or “y” again and pass it to the left.

f(x)=(x-4) 2 -9

Note: “f(x)” and “y” are the same.

You converted it!