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? Check all that apply.

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.
Victor’s graph has a y-intercept of 4.

Answer 1

Answer: 1, 3, 5

Explanation:

Answer 2

Answers:

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.

Ava’s graph has a y-intercept of 4.

Given:

Ava graphs the function
`h(x) = x^2 + 4`.

Victor graphs the function
`g(x) = (x + 4)^2`

To find y intercept we plug in 0 for x

`h(x) = x^2 + 4`

`h(x) = 0 + 4`= 4

So ,Ava’s graph has a y-intercept of 4.

Ava graphs the function
`h(x) = x^2 + 4`

If any number is added at the end then the graph will be shifted up. 4 is added at the end so there will be vertical translation.

Hence , Ava’s graph is a vertical translation of f(x) = x^2. Also Ava moved 4 units up from f(x) = x^2 in a positive y- direction.

Victor graphs the function
`g(x) = (x + 4)^2`

If any number added with x then the graph will be shifted left. the graph will be shifted in negative x direction.