express y=4x²-2x+5, in the form y=A+B(x+C)²

Question

A homework

Answer 1

y=A+(Bx+C)^2=A+B^2x^2+2BCx+C^2 has to be equivalent to 4x^2-2x+5.

Equating terms we have:

x^2: B^2=4, B=±2

x: 2BC=-2, BC=-1 so C=-1/B so C=1/2 if B=-2 and C=-1/2 if B=2

Constant: A+C^2=5, so A=5-C^2, and A=5-1/4=19/4.

SOLUTION: A=19/4, (B=-2, C=1/2) or (B=2, C=-1/2)

y=4x^2-2x+5=19/4+(2x-1/2)^2 or y=19/4+(1/2-2x)^2.