Intro to Quadratics and Polynomials + Addition and Subtraction

INDETERMINATES AND COEFFICIENTS, THAT

INVOLVES ONLY THE OPERATIONS OF ADDITION,
SUBTRACTION, MULTIPLICATION, AND POSITIVE-

INTEGER POWERS OF VARIABLES.

QUADRATICS ARE THE MAIN TYPE OF POLYNOMIAL

PHYSICS

ENGINEERING
ECONOMICS
BUSINESS

COMPUTER GRAPHICS

GRAPHIC DESIGN

FINANCE
BIOLOGY

STATISTICS
ASTRONOMY
GEOMETRY

MEDICINE / MEDICAL FIELD

ART AND MUSIC
COSMETOLOGY
ART AND MUSIC

ENVIRONMENTAL SCIENCE

POLYNOMIALS:

Open Ended

What is one real world use of polynomials or quadratics?

POLYNOMIALS CAN EXIST WITH ONLY A SINGLE TERM.

POLYNOMIALS WITH ONE TERM ARE CALLED “MONOMIALS”
POLYNOMIALS WITH TWO AND THREE TERMS ARE CALLED

“BINOMIALS” AND “TRINOMIALS

Multiple Choice

Polynomials can exist with as low as _____ terms?

• One

• Two

• Three

• Four

Multiple Select

Polynomials with two or three terms are referred to as:

• Binomials

• Monomials

• Trinomials

TERMS: THE BUILDING BLOCKS OF POLYNOMIALS. EACH TERM IS POSSIBLY MADE UP

OF A COEFFICIENT, A VARIABLE, AND A DEGREE.

COEFFICIENT: THE COEFFICIENT OF A TERM IS THE NUMBER, TYPICALLY FOUND IN

FRONT OF A VARIABLE.

VARIABLE: VARIABLES, AS YOU PROBABLY ALREADY KNOW, ARE LETTERS THAT
REPRESENT NUMBERS. THE LETTER WE USE AS A VARIABLE MOST OFTEN IS X.

CONSTANT: THE CONSTANT TERM OF A POLYNOMIAL IS THE TERM

(IF THERE IS ONE) WITH NO VARIABLE.

DEGREE: THE DEGREE OF A TERM IS EQUAL TO THE NUMBER THAT THE VARIABLE
IS RAISED TO. THE ONLY POWER YOU CAN RAISE TO WHERE IT WILL DISAPPEAR IS
0 BECAUSE ANYTHING TO THE ZERO POWER IS 1, SO THE DEGREE IS 0. THE DEGREE

IS NEVER NEGATIVE, AND NEVER A FRACTION.

QUADRATIC FUNCTIONS ARE...

ANY FUNCTIONS DEFINED BY THE EXPRESSION:

THIS IS THE “GENERAL FORM” OF QUADRATIC FUNCTIONS

QUADRATIC FUNCTIONS:

A, B, AND C ARE THE CONSTANTS OF THE

FUNCTION, WHICH DETERMINE THE SHAPE AND

POSITION OF EACH FUNCTIONS GRAPH

Multiple Select

What are the constants of the quadratic function in general form?

• A

• B

• C

• X

GENERAL FORM:

IN GENERAL FORM, THE
CONSTANTS B AND C CAN

HAVE ANY VALUES

INCLUDING: POSITIVE,
NEGATIVE, AND ZERO

GENERAL FORM:

IN GENERAL FORM, THE
CONSTANTS B AND C CAN

HAVE ANY VALUES

INCLUDING: POSITIVE,
NEGATIVE, AND ZERO

IF THE CONSTANT A WERE
TO EVER BE FROZEN, THE
FUNCTION WOULD HAVE NO

X SQUARED TERM AND

GENERAL FORM:

IN A QUADRATIC FUNCTION,

‘A’ CAN NOT EQUAL ZERO

Multiple Choice

Which variables can equal to zero and which can not?

• A can equal to zero, but B and C cannot.

• B can equal to zero, but A and C cannot.

• B and C can equal to zero, but A cannot.

• A and C can equal to zero, but B cannot.

Multiple Choice

If a functions 'a' were to be zero, it would be what type of function?

• Linear, not quadratic.

• Quadratic, not linear.

Poll

Quadratic functions must always contain:

• Any X term

• Any X squared term

WHEN A QUADRATIC FUNCTION IS

GRAPHED, IT ALWAYS MAKES A SHAPE

OF A PARABOLA

THE POINT WHERE THE PARABOLA

CHANGES DIRECTION, ALSO REFERRED
TO AS THE TURNING POINT, IS CALLED

THE VERTEX OF THE QUADRATIC

THE POINT WHERE THE PARABOLA

CHANGES DIRECTION, ALSO REFERRED
TO AS THE TURNING POINT, IS CALLED

THE VERTEX OF THE QUADRATIC

THE VERTICAL LINE

THAT INTERSECTS THE
VERTEX IS CALLED THE

AXIS OF SYMMETRY

DEPENDING ON THE VALUES OF A, B, AND C, THE
PARABOLA MAY BE PLACED ANYWHERE ON THE

COORDINATE PLANE

THE DIRECTION THAT THE PARABOLA OPENS IN

DEPENDS ON THE VALUE OF ‘A’

IF THE PARABOLA OPENS

DOWNWARD, A IS NEGATIVE

IF THE PARABOLA OPENS
UPWARD, A IS POSITIVE

Multiple Choice

The direction that the parabola opens in depends on the variable:

• A

• B

• C

• X

ADDING AND SUBTRACTING

POLYNOMIALS

TO HELP YOU ANSWER AN ADDITION OR

SUBTRACTION PROBLEM WITH

POLYNOMIALS,

1) YOU NEED TO STACK THE TWO

EQUATIONS WITH LIKE TERMS PUT

TOGETHER.

2) THEN YOU WILL ADD OR SUBTRACT

PLACE ZEROS AS
PLACEHOLDERS IN

POLYNOMIAL
EXPRESSIONS.