Modulus and Quadratic functions

Author:
Mr. Wright
Finding roots of quadratic and modulus functions
The task is to investigate how translations affect the roots of quadratic and modulus functions. This geogebra worksheet plots f(x)=(x+p)^2+q and g(x)=|x+r|+s. Some prompt questions are below. How are the graphs similar and how are they different? What values can q take so that the quadratic has at least one root? What is the relationship between p and q (or r and s) and the minima? When do the modulus and the quadratic functions have the same roots? What values of p and q (or r and s) give the root x=0? What about x = 1, 2 or 5? What is the relationship between the sliders and the roots?