ava graphs the function $h(x) = x^2 + 4$. victor graphs the function $g(x) = (x + 4)^2$. which statements…

To solve this, we analyze the transformations of the parent function ( f(x) = x^2 ):

Step 1: Analyze Ava's function ( h(x) = x^2 + 4 )

The general form for vertical translation of ( f(x) = x^2 ) is ( f(x) = x^2 + k ), where ( k ) is the vertical shift. If ( k>0 ), it is a vertical shift up (positive direction). For ( h(x) = x^2 + 4 ), comparing with ( f(x) = x^2 ), we have ( k = 4 ). So, Ava’s graph is a vertical translation (shift up by 4 units) of ( f(x) = x^2 ). Thus, the statement "Ava’s graph is a vertical translation of ( f(x) = x^2 )" is true, and "Ava’s graph moved 4 units from ( f(x) = x^2 ) in a positive direction" is also true (since moving up 4 units is positive vertical direction).

Step 2: Analyze Victor's function ( g(x) = (x + 4)^2 )

The general form for horizontal translation of ( f(x) = x^2 ) is ( f(x) = (x - h)^2 ), where ( h ) is the horizontal shift. If ( h<0 ), it is a shift to the left. For ( g(x) = (x + 4)^2=(x - (-4))^2 ), comparing with ( f(x) = x^2 ), we have ( h=-4 ), which means a horizontal shift left by 4 units (not a vertical translation). So, the statement "Victor’s graph is a vertical translation of ( f(x) = x^2 )" is false.

So the three correct statements (assuming there are more options, but from the given ones here, the first, third (Ava’s graph moved 4 units...), and we assume there are other correct ones, but from the visible options:

1. Ava’s graph is a vertical translation of ( f(x) = x^2 ) - True
2. Victor’s graph is a vertical translation of ( f(x) = x^2 ) - False
3. Ava’s graph moved 4 units from ( f(x) = x^2 ) in a positive direction - True

(Note: Since the problem says "Choose three correct answers" and only three options are visible here, we assume these three are the ones, but if there are more options, we need to check. But from the given visible options, the correct ones are:

• Ava’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

And one more (if there are more options, but with the given three, two are true, but the problem says three, so maybe there are other options not visible. But based on the visible ones, the two true ones are the first and the third, and if we assume a third true one from other (invisible) options, but with the given, we can conclude the two visible true ones and one more. However, from the visible:

The correct answers (from the visible options) are:

• Ava’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

(And if there is a third, like maybe a statement about Victor’s graph being horizontal translation, but since the visible options have only three, and two are true, but the problem says three, so perhaps there is a typo or more options. But with the given, the two true ones are the first and the third, and we assume the third is correct.)

Final Answer (the three correct statements from visible options, assuming):

1. Ava’s graph is a vertical translation of ( f(x) = x^2 )
2. Ava’s graph moved 4 units from ( f(x) = x^2 ) in a positive direction
   (And one more, but with the given, these two are correct, and if we consider the problem’s instruction to choose three, we might have missed one, but with the given, these are the two true ones from the visible.)