standard_description: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
problem_activity: Warm-up
In this warm-up, students revisit quadratic expressions in different forms and what the expressions reveal about the graphs that represent them. They match equations and graphs representing two quadratic functions. The axes of the graphs are unlabeled, so students need to reason abstractly about the parameters in the expressions and the features of the graphs.
Student Facing
[IMG]
Here are graphs representing the functions
\(f\)
and
\(g\)
, given by
\(f(x) = x(x+6)\)
and
\(g(x) = x(x+6)+4\)
.
Which graph represents each function? Explain how you know.
Where does the graph of
\(f\)
meet the
\(x\)
-axis? Explain how you know.
Student Response
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Activity Synthesis
Invite students to share their matches and explanations. If one or more explanations in the Student Response are not mentioned, bring them up so that students can see multiple ways of reasoning about the equations and graphs.


aligns: no