Piecewise and Quadratic Functions
Teacher: Labor
CA Standard(s):
Date: 8/26 - 30
Subject/Course: Pre-Calculus
Grade: 11th/12th
Alg 1 6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch
the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
Alg 1 7.0 tudents verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using
the point-slope formula.
Alg 2 1.0 Students solve equations and inequalities involving absolute value.
Alg 2 8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students
apply these techniques in solving word problem. They also solve quadratic equations in the complex number system.
Alg 2 10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function.
Alg 2 25.0 Students use properties from number systems to justify steps in combining and simplifying functions.
Learning Objective (s):
Given a piecewise function, the learner will graph the function by graphing each individual sub-function.
Given a quadratic function, the learner will find its maximum or minimum value by using a formula to find its vertex.
Given a quadratic function, the learner will find its x-intercepts by finding its zeros using either factoring or the quadratic formula.
Given a quadratic function, the learner will graph the function by first finding its intercepts and vertex.
Given a quadratic function with complex roots, the learner will graph the function by first finding its vertex and using a table of values.
Essential Question(s):
What is a piecewise function?
What is domain?
How do you use the domain of a piecewise function to sketch its graph?
How does the vertex of a parabola relate to the quadratic’s minimum or maximum value?
How do you find the zeros of a quadratic function?
Will there always be x-intercepts for all quadratic equations?
Assessment:
Homework quiz on day 1, quick check on all days.
Do Now: Writing prompts:
Day 1: “The slope of a line can tell you…”
Day 2: “A piecewise function is a function…”
Day 3: A quadratic function is…”
WHOLE GROUP
Do Now: Writing Promts
Lesson: Note-taking (I Do, You Do, We Do): Graphing Piecewise functions and Quadratic Functions
Quick Check
DIRECT INTRUCTION STATION
Unit 2: Polynomial Functions
Notes: Interactive lecture piecewise and
quadratic functions. Students use their
composition notebooks to copy notes. Students
then answer guided exercises and then answer
problems on their own.
Activities:
*Note-taking
*Pair-share
*Mini-whiteboards
*Thumbs up, thumbs down
*I Do, You Do, We Do
*Quick checks
Address possible misconceptions:
*Linear equations: incorrectly identifying the
slope from a given equation
*Linear equations: using a wrong formula to find
the slope (switching the numerator and
denominator)
*Plotting points: incorrectly identifying the
horizontal distance from the vertical distance by
using the wrong number from an ordered pair
*Simplifying fractions: Difficulty dealing with
fractions with different denominators.
*Quadratic Functions: Wrong factors
*Quadratic Functions: Parabola Opening is
reversed
*Quadratic Functions: Unfamiliar with complex
COLLABORATIVE STATION
Exploration: Students will be assigned to groups
of 3 or 4 depending on the result of quick checks
or verbal assessments. Students will be working
on graphing piecewise functions.
Group Roles:
Leader: Moderates the whole group and
ensures that each member is doing his/her role
Time Keeper: Ensures that each member is on
efficiently on track to accomplish the task
Recorder: Records all responses and makes
sure every one in the group shares the same
data
Reporter: Shares what the group learned from
the activity
INDEPENDENT STATION
Homework Quiz #5: On day 1, students will be
given problems from assigned homework from
the previous day to check for comprehension.
Individual work: Each student is assigned
homework to build on the concepts discussed in
class.
Day 1 HW:
p41 #80 - 84
p97 #32 – 34 (graph only)
Day 3 HW:
p97 #26, 35
p76 #23, 24
*All HW answers need to be in a composition
notebook
roots