Answer:
[tex]f(x)=(x+6)^2[/tex]
Step-by-step explanation:
We have been given that the parabola touches the x-axis at the zero x = -6.
Whenever, the graph touches the x axis at any zero and returns back then the multiplicity of that zero is even.
On the other hand if the graph crosses the x axis at any zero then the multiplicity of the zero will be odd.
Now, parabola touches the x-axis at the zero x = -6 hence, the multiplicity of the zero is even. Since, it is a quadratic function hence, the multiplicity will be 2.
The zero is x = -6 hence, the factor would be (x+6).
Therefore, the function is [tex]f(x)=(x+6)^2[/tex]
