The graph of the function y = x² + 3 is shown below.

If the graph of the original function is shifted 4 units down, which of the following equations best represents the translation of each point on the curve?

A. y = x² − 4
Incorrect. The original value of c is 3 and the function is being shifted down 4 units.

B. y = x² − 1
Correct! The original vertex was at (0, 3) and a shift of 4 units down would change the vertex to (0, –1).

C. y = x² + 4
Incorrect. The original value of c is 3 and the function is being shifted down 4 units.

D. y = x² + 7
Incorrect. The original value of c is 3 and the function is being shifted down 4 units.

If the graph of the function y = x² − 1, the -5 is changed to 1, which description explains the shift in the vertex of the parabola?

A. 6 units up
Correct! A change in the vertex from -5 to 1 would shift the parabola 6 units up.

B. 1 unit up
Incorrect. The value of c is being changed from -5 to 1.

C. 1 unit down
Incorrect. The value of c is being changed from -5 to 1.

D. 6 units down
Incorrect. The value of c is being changed from -5 to 1.

When graphed, which function would appear to be shifted 3 units up from the graph of f(x) = x² − 1?

A. g(x) = x² − 4
Incorrect. The parabola is being moved 3 units up from -1.

B. g(x) = x² − 3
Incorrect. The parabola is being moved 3 units up from -1.

C. g(x) = x² + 2
Correct! The parabola is being moved 3 units up.

D. g(x) = x² + 3
Incorrect. The parabola is being moved 3 units up from -1.

Which graph shows a function y = x² + c when c > 1?

A.	C.
B.	D.

A.
Incorrect. The value of c is 0.

B.
Incorrect. The value of c is -3.

C.
Incorrect. The value of c is 1.

D.
Correct! The value of c >1.

How would the graph of the function y = x² − 6 be affected if the function were changed to y = x² − 8?

A. The graph would shift 8 units down.
Incorrect. The graph of parabola is being moved 2 units down from -6.

B. The graph would shift 2 units down.
Correct! The graph of the parabola is being moved 2 units down from -6.

C. The graph would shift 2 units up.
Incorrect. The graph of parabola is being moved 2 units down from -6.

D. The graph would shift 8 units up.
Incorrect. The graph of parabola is being moved 2 units down from -6.