Answer:
[tex]y=x^{2}+6x+9[/tex]
[tex]y=-x^{3}[/tex]
[tex]y=(x+2)(x+6)^{2}[/tex]
[tex]y=(x-5)(x+3)(x+1)(x-5)[/tex]
[tex]y=x^{4}[/tex]
Step-by-step explanation:
we know that
If the graph is tangent to the x-axis at one of its intercepts
then
the vertex of the graph or the inflection point of the graph lie on the x-axis
using a graphing tool
Verify each case
case A) [tex]y=x^{2}+6x+9[/tex]
The case A) has a graph that is tangent to the x-axis at one of its intercepts
case B) [tex]y=-x^{3}[/tex]
The case B) has a graph that is tangent to the x-axis at one of its intercepts
case C) [tex]y=(x+2)(x+6)^{2}[/tex]
The case C) has a graph that is tangent to the x-axis at one of its intercepts
case D) [tex]y=(x-5)(x+3)(x+1)(x-5)[/tex]
The case D) has a graph that is tangent to the x-axis at one of its intercepts
case E) [tex]y=x^{4}[/tex]
The case E) has a graph that is tangent to the x-axis at one of its intercepts
