Answer: To compare the two functions, we can analyze their algebraic properties:
h(x) = x^2 + 4 can be obtained by vertically shifting the function f(x) = x^2 upward by 4 units.
g(x) = (x + 4)^2 can be obtained by horizontally shifting the function f(x) = x^2 left by 4 units.
Therefore, the following statements are true:
Ava’s graph is a vertical translation of f(x) = x^2.
Victor’s graph is a horizontal translation of f(x) = x^2.
Ava’s graph moved 4 units from f(x) = x^2 in a positive direction.
The statement "Victor’s graph moved 4 units from f(x) = x^2 in a positive direction" is not true because the shift is horizontal, not vertical.
The statement "Ava’s graph has a y-intercept of 4" is also not necessarily true, as the y-intercept of h(x) = x^2 + 4 is (0,4), but the function could be shifted up or down depending on the constant added to x^2.
Explanation: