Does anyone know how to do the bottom question in the attachment below?

If you notice from section a), by completing the square, you really ended  up with the "vertex form of a parabola".

where's the vertex anyway?  check the picture below.

now, the parabola has a leading term, namely x²,  with a positive coefficient, that means the parabola opens upwards, as in the picture.

so f(x), or namely "y", gets values from y = 4, 5, 6 , 7 .... +∞, since it goes up and up and up, and never down.  Since it began above the x-axis, is never negative, since it never goes below 4 anyway.

The answer is c drawing a