Question

possible points: 25
identify the transformation and vertex of the function $g(x) = -6(x + 4)^2 - 3$ from the parent function $f(x) = x^2$. move the correct answer to each box. not all answers will be used.
the transformation of f(x) to g(x) is a horizontal shift 4 units left , a vertical shift 3 units down and a
the graph of g(x) is than the graph of f(x).
the vertex is (-4,-3)
options: reflection across the x-axis, reflection across the y-axis

Explanation:

Step1: Identify reflection transformation

The coefficient of the squared term in $g(x)$ is $-6$, which is negative. For the parent function $f(x)=x^2$, a negative coefficient outside the squared term means a reflection across the x-axis.

Step2: Compare graph vertical stretch

The absolute value of the coefficient $|-6|=6>1$, so the graph of $g(x)$ is narrower than $f(x)$.

Answer:

The transformation of $f(x)$ to $g(x)$ is a horizontal shift 4 units left, a vertical shift 3 units down and a reflection across the x-axis
The graph of $g(x)$ is narrower than the graph of $f(x)$
The vertex is $(-4,-3)$