Question

use transformations to graph the function.
\\( v(x) = -(x + 4)^2 - 2 \\)
part: 0 / 2
part 1 of 2
the graph of \\( v(x) = -(x + 4)^2 - 2 \\) is the same as the graph of \\( f(x) = x^2 \\) with three transformations in the follo

1. select
2. select
3. select

Explanation:

Step1: Identify reflection transformation

The negative sign outside $(x+4)^2$ reflects $f(x)=x^2$ over the x-axis: $f_1(x) = -x^2$.

Step2: Identify horizontal shift transformation

Replacing $x$ with $x+4$ shifts $f_1(x)$ left 4 units: $f_2(x) = -(x+4)^2$.

Step3: Identify vertical shift transformation

Subtracting 2 shifts $f_2(x)$ down 2 units: $v(x) = -(x+4)^2 - 2$.

Answer:

1. Reflect the graph of $f(x)=x^2$ over the x-axis
2. Shift the resulting graph 4 units to the left
3. Shift the resulting graph 2 units downward