Answer:
[tex]f(x) = -5(x+1)^2[/tex]
Step-by-step explanation:
We are given the following function:
[tex]f(x) = x^2[/tex]
Shift 1 unit right.
Shifting a function a units to the right is finding f(x+a). So
To shift one unit right:
[tex](x+1)^2[/tex]
Vertically stretch by a factor of 5.
To vertically stretch by a factor of 5, we multiply the function by 5. So
[tex]5(x+1)^2[/tex]
Reflect over the x-axis.
To reflect over the x-axis we multiply the function by -1. So
[tex]f(x) = -5(x+1)^2[/tex]