Answer:

Vertex form: a(x-h)²+k

1. y=x²+5x

> y+?=(x²+5x+(5/2)²)

> y+?=(x²+5x+25/4)

> y+25/4=(x²+5x+25/4)

> y+25/4=x²+5x+25/4

> y=(x+5/2)²-25/4

> y=(x+5/2)²-25/4

2. y=-2x²-8x

> y+?=-2(x²-4x+(-4/2)²)

> y+?=-2(x²-4x+4)

> y+(-2)4=-2(x-2)²

> y+(-8)=-2(x-2)²

> y=-2(x-2)²+8

3. y=x²-4x+5

> y+?=(x²-4x+(-4/2)²)+5

> y+?=(x²-4x+4)+5

> y+4=(x²-4x+4)+5

> y+4=(x-2)²+5

> y=(x-2)²+5-4

> y=(x-2)²+1

4. y=-3x²-x-8

> y+?=-3(x²-x+(-1/2)²)-8

> y+?=-3(x²-x+1/4)-8

> y+-3(1/4)=-3(x-1/6)²-8

> y+(-3/4)=-3(x-1/6)²-8

> y=-3(x+1/2)²-8(3/4)

> y=-3(x+1/2)²-6