Graph of the function

Question

The graph of is f(x)=(x-9)^2+7 is which of the followings:

 

1. shifted 9 unit to the right of y=x^2 and up 7 units.
2. shifted 9 unit to the left of y=x^2 and up 7 units.
3. shifted 9 unit to the right of y=x^2 and down 7 units.
4. shifted 9 unit to the left of y=x^2 and down 7 units.

Answer 1

You have the form

 

f(x) = g(x - a) + b

 

where a and b are positive.  This corresponds to a shift of a units to the right, and b units up.  In this case, the parabola for x² is shifted 9 units to the right and 7 units up, which is answer (1).  If b was negative, you shift down.  If you had g(x + a) with a positive, you shift left.

 

Answer 2

1. shifted 9 units to the right of y=x^2 and up 7 units.

You can verify this by imagining when the squared quantity equals zero, corresponding to the vertex of y =x²; the vertex is now at x=9, nine units (plural) to the right of its 'nominal' location.