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Ava graphs the function h(x) = x^2 + 4. Victor graphs the function g(x) = (x + 4)^2. Which statements are true regarding the two graphs? Select three options. Ava’s graph is a vertical translation of f(x) = x^2. Victor’s graph is a vertical translation of f(x) = x^2. Ava’s graph moved 4 units from f(x) = x^2 in a positive direction. Victor’s graph moved 4 units from f(x) = x^2 in a positive direction. Ava’s graph has a y-intercept of 4.

User ZeppRock
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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:

User Sheena Singla
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