Question

Ava graphs the function h(x) = x2 + 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) = x2.
Victor’s graph is a vertical translation of f(x) = x2.
Ava’s graph moved 4 units from f(x) = x2 in a positive direction.
Victor’s graph moved 4 units from f(x) = x2 in a positive direction.
Ava’s graph has a y-intercept of 4.

Answer 1

Correct choices: 1, 3, and 5.

- h(x) = x^2 + 4 is f(x)=x^2 shifted vertically up by 4, so (1) true.
- That shift is 4 units in the positive (upward) direction, so (3) true.
- h(0) = 0^2 + 4 = 4, so the y-intercept is 4, making (5) true.
- g(x) = (x+4)^2 is a horizontal shift left 4, not a vertical translation and not a positive/rightward shift, so (2) and (4) are false.