options: Understand the concept of a function and use function notation.

Interpret expressions for functions in terms of the situation they model.

Interpret functions that arise in applications in terms of the context.

Prove and apply trigonometric identities.

Model periodic phenomena with trigonometric functions.

Analyze functions using different representations.

Extend the domain of trigonometric functions using the unit circle.

Use functions to model relationships between quantities.

Build a function that models a relationship between two quantities.

Build new functions from existing functions.

Define, evaluate, and compare functions.

Construct and compare linear and exponential models and solve problems.
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
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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
\(x=0\)
.


correct_option_index: 5