# Quadratic Equations Lesson Plan 2

Objectives: Students will learn to identify and sketch the general forms of quadratic
equations. The student learns the affects on the graph of changes in the leading
coefficient and the constant term.

Materials:
Teacher: small foam ball
Dry erase board and marker
TI-83+ view screen
Students: graph paper (provided by student)
Pencil (provided by student)

Introduction: (Engage and Explore): Begin the lesson by reviewing the concepts
learned in the previous lesson , specifically that quadratics are polynomials of degree two .
Write the general formula for a quadratic on the board. Next take the small ball and toss
it in the air and catch it with the other hand at the same height. Ask the students to draw
what the see as the path of the ball.

Procedures: After the students sketch the graph, put a polynomial equation on the board
and have the students pick random values of x and determine the corresponding y values.
Then have them plot the points on their graph paper. Make sure that they get points from
both sides of the parabola . Do this a few times (make sure that some have positive and
some have negative leading coefficients.) until students get the right idea about the shape
of the graph.

Now have the students graph y = x2 on their calculator while you do the same on the
view-screen. Then have them graph y = 5x2 on the same screen. Have the students
discuss what happens when ‘a’ is changed, when ‘c’ is changed and when everything is
multiplied by negative 1.

Adaptations: If there are not enough calculators for everyone, divide the class into small
groups and let them work together with one calculator.

Discussion Questions: Ask students how they can find the minimum or maximum point?
Let them hypothesis on what coefficients change the location of the vertex .

Assessment/Evaluation: Students will show mastery of concepts through worksheets and
tests.

Extensions: Assign a few homework problems to be graphed by hand and by calculator.

Suggested Readings: Alexander, Bob Explore Quadratic Functions with the TI-83 or TI-
82, 1997

ξ111.32.a. (5)
Tools for algebraic thinking. Techniques for working
with functions and equations are essential in understanding underlying relationships.
Students use a variety of representations (concrete, numerical , algorithmic, graphical),
tools, and technology, including, but not limited to, powerful and accessible hand-held
calculators and computers with graphing capabilities and model mathematical situations
to solve meaningful problems.

:ξ111.32.d(1) The student understands that the graphs of quadratic
functions are affected by the parameters of the function and can interpret and describe the
effects of changes in the parameters of quadratic functions.

Time of Lesson: 1 50-minute lesson

Tips on teaching: Instead of tossing a ball from one hand to another, have the students
toss the ball back and forth to each other.

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