Answer:
\(y=x^{2}+6x+9\)
\(y=-x^{3}\)
\(y=(x+2)(x+6)^{2}\)
\(y=(x-5)(x+3)(x+1)(x-5)\)
\(y=x^{4}\)
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) \(y=x^{2}+6x+9\)
The case A) has a graph that is tangent to the x-axis at one of its intercepts
case B) \(y=-x^{3}\)
The case B) has a graph that is tangent to the x-axis at one of its intercepts
case C) \(y=(x+2)(x+6)^{2}\)
The case C) has a graph that is tangent to the x-axis at one of its intercepts
case D) \(y=(x-5)(x+3)(x+1)(x-5)\)
The case D) has a graph that is tangent to the x-axis at one of its intercepts
case E) \(y=x^{4}\)
The case E) has a graph that is tangent to the x-axis at one of its intercepts
