need help as soon as possible please!

Question

verify, in at least two different ways,that the two algebraic forms in each pair represent the same function.

1. y=x²-22x+13 and y=(x-11)²-108

2. y=4x²+120x and y=4(x+15)²-900

3.y=9x² - 54x - 10 and y= 9(x-3)² -91

4.y=-4x²-8x+2 and y= -4(x+1)² +6

 

i need your help please :(((((

our topic is completing the square

Answer 1

We aren't doing your homework for you.  I'll do one, but you need to do the rest.

1), way 1

x^2 - 22x + 13

There's a -22 on the x.  Half of -22 is -11.  -11 squared is 121.

x^2 - 22x + 121 - 121 + 13

(x - 11)^2 - 108

.

1), way 2

(x - 11)^2 - 108

x^2 - 11x - 11x + 121 - 108

x^2 - 22x + 13