Question

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.

Answer 1

Given,

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

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

Required:

Check the correct statement about graph.

The graph of Ava and vector function is:

Here, victor graph was represented by blue curve and ava graph by green curve.

For first statement,

Ava’s graph is a vertical translated by 4 units.

Hence, statement is true.

For second statement,

The graph of victor is not vertically translated.

Hence, statement is false.

For statement three,

The curve of the Ava graph is moved 4 unit up in the positive direction. It is in y axis. Hence, statement is true.

For statement forth,

The curve of the victor graph is moved to negative direction not positive. Hence, statement is false.

For statement fifth,

The graph of Ava has the y intercept at 4. So, statement is correct.

Hence, option A (Ava’s graph is a vertical translation of f(x) = x^2), option C (Ava’s graph moved 4 units from f(x) = x^2 in a positive direction) and option E (Ava’s graph has a y-intercept of 4.) is true.