Explanation
We are required to identify any horizontal or vertical translations in the given function below:
[tex]f(x)=1-(x+3)^2[/tex]
This is achieved thus:
First, the function can be rewritten as:
[tex]f(x)=-(x+3)^2+1[/tex]
We know that the vertex form of a quadratic function is given as:
[tex]\begin{gathered} f(x)=a(x-h)^2+k \\ where \\ (h,k)\text{ }is\text{ }the\text{ }vertex \end{gathered}[/tex]
We also know that the following translation rules exist:
Therefore, we can conclude the following on the given function:
• The function reflects on the x-axis.
,
• The function shift 3 units to the left.
,
• The function shifts 1 unit upwards.
Hence, the answers are:
[tex]\begin{gathered} Horizontal:3\text{ }units\text{ }to\text{ }the\text{ }left \\ Vertical:1\text{ }unit\text{ }up \end{gathered}[/tex]
