Question

describe how the graph of the function $y = -(x + 4)^2 - 6$ is related to the graph of the parent function.
vertical translation: select choice
horizontal translation: select choice
dilation: select choice
reflection: select choice

Explanation:

Step1: Identify parent function

The parent function for this quadratic is $y=x^2$.

Step2: Analyze vertical translation

Look at the constant term $-6$: subtract 6 means shift down 6 units.

Step3: Analyze horizontal translation

Look at $(x+4)$: $x-h$ form, so $h=-4$, shift left 4 units.

Step4: Analyze dilation

The coefficient of the squared term is $-1$, absolute value 1 means no dilation (no stretch/compression).

Step5: Analyze reflection

The negative sign in $-(x+4)^2$ reflects over the x-axis.

Answer:

vertical translation: 6 units down
horizontal translation: 4 units left
dilation: No dilation (no stretch or compression)
reflection: Reflected over the x-axis