ava graphs the function h(x) = x² + 4. victor graphs the function g(x) = (x + 4)². which statements are true…

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.\n□ avas graph is a vertical translation of f(x) = x².\n□ victors graph is a vertical translation of f(x) = x².\n□ avas graph moved 4 units from f(x) = x² in a positive direction.\n□ victors graph moved 4 units from f(x) = x² in a positive direction.\n□ avas graph has a y - intercept of 4.

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.\n□ avas graph is a vertical translation of f(x) = x².\n□ victors graph is a vertical translation of f(x) = x².\n□ avas graph moved 4 units from f(x) = x² in a positive direction.\n□ victors graph moved 4 units from f(x) = x² in a positive direction.\n□ avas graph has a y - intercept of 4.

Answer

Explanation:

Step1: Recall translation rules

For a function $y = f(x)+k$, it is a vertical translation of $y = f(x)$. For $y=f(x + h)$, it is a horizontal translation of $y = f(x)$.

Step2: Analyze Ava's graph

Ava has $h(x)=x^{2}+4$. Since $h(x)=f(x)+4$ where $f(x)=x^{2}$, it is a vertical translation of $f(x)=x^{2}$ and it moves 4 units up (positive direction). When $x = 0$, $h(0)=0^{2}+4=4$, so the $y$-intercept is 4.

Step3: Analyze Victor's graph

Victor has $g(x)=(x + 4)^{2}=f(x + 4)$ where $f(x)=x^{2}$, it is a horizontal translation of $f(x)=x^{2}$ 4 units to the left (negative $x$-direction).

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.