Question

Which of the following is 3 units lower than y = 4x2 – 8x + 2, but opens in the same direction and has the same shape?

Answer 1

Simplify the function
`y=4x^2-8x+2` in the following way:

`y=4x^2-8x+2=4x^2-8x+4-4+2=4(x^2-2x+1)-2=4(x-1)^2-2.`

If you have to translate the graph of the function 3 units lower (down), then

`y=4(x-1)^2-2-3=4(x-1)^2-5.`

The graph of obtained function opens in the same direction as the graph of the function
`y=4(x-1)^2-2.`

Answer:
`y=4(x-1)^2-5.`