Activity Set 3.2CLASS PPTX

Visual Algebra for Teachers

Chapter 3

REAL NUMBERS AND QUADRATIC FUNCTIONS

Visual Algebra for Teachers

Visual Algebra for Teachers

Activity Set 3.2

Introduction to Quadratic Functions

Black and red tiles, white and opposite white n-strips and black and red x-squares

Graphing calculator with table functions (recommended)

MATERIALS

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#1

Explain why we use black x-squares and red x-squares instead of white and opposite white x-squares.

Follow up to Prep 3.2

e) Fill out the indicated function values in the following t-table.

f) By looking at the symbolic form of the function y = f(x), what do you think the range of y = f(x) is? Give this range on a number line and using inequality notation.

Question #2ef

x -2 -1.5 -1 -.5 -.25 0 .25 .5 1 1.5 2 x

f(x)

g) Label the axes with appropriate numbers, plot ALL of the coordinate pairs from your t-table and sketch y = f(x).

Notice that, unlike the absolute value graphs, the “bottom” of this graph does not come to a sharp point.

Question #2g

h) How does your answer for part f. about range show visually on the graph in part g.? Explain the connection.

i) How does your answer for part d. show visually on the graph in part g. (even though the answer may be off of the grid given in part g.)? Explain the connection.

j) What are the coordinates for the lowest point (called the Turning Point) on the graph of y = f(x)? How is this connected to the range of the function?

Question #2hij

A polynomial of degree n is a function of the form

where the coefficients (the numbers in front of the variables) a0, … an are real numbers, an ≠ 0, and the powers of x; 1, … , n are positive counting numbers.

The degree of a polynomial is its highest power of x.

The leading coefficient is the coefficient of the term of the polynomial with the highest power.

Question #3: Definitions

1 11 1 0( ) ...n n

n np x a x a x a x a

The graph you have sketched in activity 2 is a parabola.

Parabolas are the graphs of quadratic functions.

All quadratic functions are polynomials of degree two and have a turning point which is either the lowest or the highest point on the parabola.

Question #3: Definitions

a. Explain how the function f(x) in activity 2 can be thought of as a polynomial of degree two.

b. Explain how any quadratic function modeled with ±x-squares, ±x-strips and black or red tiles can be thought of as a polynomial of degree two.

c. Explain how any linear function is a polynomial of degree one. How does this relate to an algebra piece model of a linear function?

Question #3: Class discussion

Classwork (in teams, as assigned)

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#5

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Homework

HW Quiz (3.2) due before 2 p.m. next class. See Moodle for HW questions (to study) and quiz

Prep PPT/Quiz (3.3) due before 2 p.m. next class. See Moodle for posted PPTX (to read) and quiz

Turn in hw (3.2) due 2 p.m. in MONDAY, WEEK 7 See HW schedule

Chapter 2 Exam is Wednesday, Week Six See Chapter 2 Practice Exam (coursepack)