Thank you for the opportunity to help you with your question!
We have the function as
Put f(x)=0 and then determine the critical value using zero factor property.
So the interval are (-infinity,1)(1,4)(4,7)(7,infinity)
We will considewr each interval and then take any arbitrary value in the interval.If the value of y in the region is less than 0 then it lies below the x-axis and if greater than 0 then it lies above the x-axis.
Consider the interval (-infinity,1)
Take x=0,y=-1*(-4)^2*(-7)^2 =-784
As the value is less than 0 therefore in this interval the y graph lies below the x axis
Consider interval (1,4)
Graph lies above the x-axis
Consider interval (4,7)\Take x=5
Graph lies above the x axis
Here also taking x=8,y>0
Graph lies above the x-axis.
So interval below the x-axis is x(- (-infinity,1)
Above the x-axis ,y(- (1,infnity)
Please let me know if you need any clarification. I'm always happy to answer your questions.