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

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.\n□ avas graph is a vertical translation of $f(x)=x^{2}$.\n□ victors graph is a vertical translation of $f(x)=x^{2}$.\n□ avas graph moved 4 units from $f(x)=x^{2}$ in a positive direction.\n□ victors graph moved 4 units from $f(x)=x^{2}$ in a positive direction.\n□ avas graph has a y - intercept of 4.

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.\n□ avas graph is a vertical translation of $f(x)=x^{2}$.\n□ victors graph is a vertical translation of $f(x)=x^{2}$.\n□ avas graph moved 4 units from $f(x)=x^{2}$ in a positive direction.\n□ victors graph moved 4 units from $f(x)=x^{2}$ in a positive direction.\n□ avas graph has a y - intercept of 4.

Answer

Answer:

A. Ava's graph is a vertical translation of $f(x)=x^{2}$. C. Ava's graph moved 4 units from $f(x)=x^{2}$ in a positive direction. E. Ava's graph has a y - intercept of 4.

Explanation:

Step1: Analyze Ava's function

The function $h(x)=x^{2}+4$ is of the form $y = f(x)+k$, where $f(x)=x^{2}$ and $k = 4$. This represents a vertical translation of $f(x)=x^{2}$ up by 4 units. When $x = 0$, $h(0)=0^{2}+4=4$, so the y - intercept is 4.

Step2: Analyze Victor's function

The function $g(x)=(x + 4)^{2}$ is of the form $y=f(x + h)$ where $f(x)=x^{2}$ and $h=4$. This represents a horizontal translation of $f(x)=x^{2}$ to the left by 4 units, not a vertical translation.