standard_description: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
problem_activity: Warm-up
This warm-up highlights the three forms of quadratic expressions students have seen so far. It reinforces how each form gives different insights into the graph of a quadratic function.
Launch
Arrange students in groups of 2. Give students a minute of quiet think time, and then ask them to share their thinking with a partner.
Student Facing
Expressions in different forms can be used to define the same function. Here are three ways to define a function
\(f\)
.
\(f(x)=x^2-4x+3\)
(standard form)
\(f(x)=(x-3)(x-1)\)
(factored form)
\(f(x)=(x-2)^2-1\)
(vertex form)
Which form would you use if you want to find the following features of the graph of
\(f\)
? Be prepared to explain your reasoning.
the
\(x\)
-intercepts
the vertex
the
\(y\)
-intercept
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Invite students to share their responses and explanations. Encourage students to name specific features of the graph of
\(f\)
. If time permits, consider asking students to use all of the info they can gather to sketch a graph.
If not already mentioned by students, point out that while the standard form allows us to find the
\(y\)
-intercept more readily, the
\(y\)
-intercept can always be found by evaluating the function at
\(x=0\)
.


aligns: no