MBF3C Quadratics II
Date: _
Factoring Trinomials of the Form x2 + bx + c
REVIEW EXPANDING
Distributive Property
Rainbow
2 x ( x 5) = 2 x 2 10x
Product of Two Binomials
FOIL
( x 3)( x + 4) = x 2 + 4 x 3 x 12
Perfect Square Binomial
Special Product
( x 5)
=
MBF3C
Date: _
Quadratics Applications
1. On Planet X, the height, h metres, of an object fired upward from the
ground at 30m/s is described by the equation h = 30t 6t2, where t
seconds is the time since the object was fired upward.
Determine
(a)
the maxim
MBF3C
Date: _
Graphing Quadratic Equations The STEP Method
Consider the graph of the basic quadratic relation y = x 2
x
y = x2
-3
9
-2
4
-1
1
0
0
1
1
2
4
3
9
What is the
vertex?
Direction of
Opening?
(0, 0)
Up
What is the STEP Pattern?
(how do you move fr
MBF3C Quadratics II
Date: _
Expanding Binomials
TERMINILOGY
Polynomial an algebraic expression made up of terms that are added and subtracted.
Term the product of a numerical coefficient and one or more variables.
Monomial a polynomial with one term.
Bino
MBF3C Quadratics II
Date: _
Factoring Trinomials (x2 + bx + c) Practice
1. Complete the following table. The first one is done for you.
Sum of the
Integers
Integers
(b)
3
2
-1
Product of
the
Integers
(c)
5
Trinomial
(Quadratic Expression)
x 2 + 5x + 6
6
9
MBF3C
Date: _
Factoring Greatest Common Factor
REVIEW TYPES OF FACTORING
1. Trinomial
Factoring
i.e. x2 + 8x + 12
2. Perfect Square
Trinomial
i.e. x2 10x + 25
Find two numbers that multiply to 25 and add to -10.
= (x 5)(x 5)
Since the two brackets are the
MBF3C Quadratics II
Date: _
Quadratic Relations: Vertex to Standard Form
Review
y = mx + b
the equation of a straight line in slope y-intercept form
Ax + By + C = 0
the equation of a straight line in Standard Equation form
Therefore
y = a ( x h )2 + k
is
MBF3C Quadratics II
Date: _
Greatest Common Factor Practice
A) Complete the following table. The first one is done for you.
Trinomial
Common Factored Form
Fully Factored Form
3x2 + 21x + 36
3(x2 + 7x + 12)
3(x+ 3)(x + 4)
2x2 + 2x 12
5x2 30x + 40
-7x2 21x
MBF3C Quadratics II
Date: _
x-Intercepts of a Quadratic Relation Practice
1. Identify the x-intercepts of each quadratic relation.
a)
b)
2. Identify the zeros of each quadratic relation.
a)
b)
3. Identify the zeros of each quadratic relation.
a) y = (x 1)
MBF3C Quadratics II
Date: _
x-Intercepts of a Quadratic Relation
x-intercepts (zeros)
roots
The _ of a quadratic equation are also called the _ of the parabola
To graph a parabola in VERTEX form, y = a ( x h ) + k , the following is needed:
2
coordinates
MBF 3C Quadratics II
Date: _
Vertex to Standard Form of a Quadratic Relation Practice
For each of the following parabolas:
1. State the vertex of the parabola
2. Expand the equation to standard form.
3. Using a graphing calculator graph each equation (the
MBF3C
Date: _
Graphing Quadratic Equations STEP Method Practice
1. Use the step method to graph
y = x2 + 2
Graph the equation.
y = x2 + 2
Equation
What is the
vertex?
Direction of
Opening?
What is the
Step Pattern?
Complete the
table of values
to CONFIRM
MBF3C
Date: _
The Quadratic Relation y = a(x-h)2 + k Practice
1. Circle the shape and orientation of each parabola and indicate the vertex.
a) y = 0.5x2 + 2
opens up / down
stretched / compressed
vertex (
,
)
b) y = 2(x 1)2
opens up / down
stretched / com