[tex]f(x)=6x^2+x^3[/tex]
Factor x square on the function on the function
[tex]f(x)=x^2\cdot(6+x)[/tex]
then, equal the expression to 0 in order to find the x-intercepts
[tex]0=x^2\cdot(6+x)[/tex]
finally, if the product is equal to 0 it means that at least one of them is equal to 0
[tex]\begin{gathered} x^2=0 \\ x=0 \\ 6+x=0 \\ x=-6 \end{gathered}[/tex]
The graph of the function touches the x-axis and turns around at
x=0,-6.
