## Reflection: High Expectations Graphs of Cubic Functions, Day 2 - Section 1: Picking Up Where We Left Off

I expect some students to struggle with the second problem because although the three roots are given, the y-intercept is not.  They will need to evaluate create an equation based on the three roots, evaluate it at x = -1 (a great opportunity to put synthetic substitution to use), and then determine the necessary constant factor.

I expect almost everyone to struggle with the third problem since, in this case, only two of the roots are given!  Encourage them to think about the structure of the equation, and to create two unknowns for the missing values.  You can see the kind of thought process I'm looking for in this student's work.  She created let r be the missing root and a the missing constant factor.  Then, with some help from classmates along the way, she was able to solve for both of them.  Conveniently, in this case a = 1!

I believe these kinds of challenges are important for students.  They push them to think more deeply about the subject and to avoid reducing it merely to a set of procedures for solving routine problems.  It's also important to bear in mind that my ultimate goal for all students is the ability to solve problems like the first one on their own.  After working through these more challenging examples, the first problem begins to look like a cake walk!

High Expectations: Upping the Ante

# Graphs of Cubic Functions, Day 2

Unit 3: Cubic Functions
Lesson 10 of 13

## Big Idea: How many points does it take to determine a cubic equation? Four - and it helps if three of them are roots!

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Subject(s):
Math, polynomial, cubic equations, Graphing (Algebra), roots (Algebra), factor theorem, Algebra 2, master teacher project, cubic functions, Algebra 2, function
45 minutes

### Jacob Nazeck

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