Mathematics TEKS Refinement 2006 – 9-12 Tarleton State University
Quadratic and Square Root Functions Algebra II
Square Roots & Quadratics: What’s the Connection? Page 2
Procedures Notes
Detailed notes are written for examining
problem i.
You may want to have groups compare
and discuss the first graph and their
results to see that they are on the right
track, or you may just want to walk the
entire class through the analysis of the first
graph.
Guide students to make their sketches
with enough detail to be able to identify
ordered pairs especially the x- and y-
intercepts of both graphs. Many students
will try to copy the graph without marking
either axis’s units or labeling any ordered
pairs. They will need these details for their
work.
3. Have the groups share their results,
and hold a class discussion of the
observations that they have made
through this investigation.
Be sure to carefully guide the discussions,
especially the results from (4) and (5).
Discuss how to restrict the domain of a
quadratic function in order to have an
inverse that is a function.
This is a good opportunity to introduce the
term one-to-one function, and illustrate
how, without a restriction on the domain, a
quadratic function does not have an
inverse that is a function.
Emphasize that a square root function is
only the inverse of a quadratic function if
the domain is restricted appropriately (to
one side of the vertex); likewise, a
quadratic function is not the inverse of a
square root function unless the domain is
appropriately restricted.
At the end of the activity, you can assist
students in deducing a procedure on how
you can find the equation of an inverse of
a function (by switching the domain and
range values of a function).