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B. Transform each quadratic function in the form y = a(x - 5)2 + k.
1. y = x2 + 2x + 1
2. y = 4x2 - 4x + 1
3. y = (x - 3)(x + 7)
4. y = x(x -9)
5. y = x2 - 2x - 48

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Answer:

1. y=x²+2x+1

> y+?=(x²+2x+(2/2)²)+1

> y+1=(x²+2x+1)+1

> y+1=(x+1)²+1

> y=(x+1)²+1-1

> y=(x+1)²

2. y=4x²-4x+1

> y+?=4(x²-x+(-1/2)²)+1

> y+1/4=4(x²-x+1/4)+1

> y+4(1/4)=4(x-1/2)+1

> y=4(x-1/2)+1-1

> y=4(x-1/2)²

3. y=(x-3)(x+7)

> y+?=x²+4x-21

> y+?=(x+4x+(4/2)²)-21

> y+4=(x+4x+4)-21

> y+4=(x+2)²-21-4

> y=(x+2)²-25

4. y=x(x-9)

> y=x²-9x

> y+?=(x²-9x+(-9/2)²)

> y+?=x²-9x+81/4

> y+81/4=(x-9/2)²

> y=(x-9/2)²-81/4

5. y=x²-2x-48

> y=(x²-2x+(-2/2)²)-48

> y+?=(x²-2x+1)-48

> y+1=(x-1)²-48-1

> y=(x-1)²-49

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