Lesson 2
Change Quadratic Relations from Vertex Form to Standard Form
Expand and simplify.
(3x + 4)(2x + 9)
Investigate
242
(7x 4)(5x 1)
(4x + 3)2
Different Forms of a Quadratic Relation
1. Find the vertex. Find the y-intercept.
a) y = (x 2)2 + 1
y = x2 4
Lesson 3
The Quadratic Relation y = a(x h)2
Recap:
1. Write an equation for a parabola that is:
a) vertically compressed and opens upward _
b) shifted up 3 units on the y-axis and opens downward _
2. Describe how each parabola compares to y = x2:
a) y = 0
Lesson 4
Factor Trinomials of the Form ax2 + bx + c
Factor and check by expanding.
x2 + 17x + 30
x2 - 81
Factor Trinomials of the Form ax2 + bx + c
x2 32x
Pp. 256 257
Complete the table. Factor each trinomial by finding the greatest common factor. Then
wr
MBF 3C
Lesson 2
The Quadratic Relation y = ax2 + k
Investigate
Graphs of y = ax2 + k
Pp. 180 182
Graph the following relationships:
y = 4x2
y = 0.5x2
y = -2x2
The Effect of Changing a
The value of a determines the orientation and shape of the parabola rel
Lesson 5
Interpret Graphs of Quadratic Equations
1. Describe the parabola defined by each quadratic relation.
a) y = 4(x 15)2 + 10
b) y = - 0.2 x2 6
2. Write an equation for the parabola graphed with the solid line.
Example 1
Use the Graph and Vertex to I
Lesson 4
Measure of Central Tendency
We will now shift our focus to calculating statistics that can be used to analyze a set of data.
Measures of central tendency provide information about the center of a set of data.
The mean is the sum of values in a se
Expand Binomials
Expand.
3(4x + 8)
Example 1
-8(7x + 9)
-5(2x 6)
3x(4x + 8)
Multiply Two Binomials
Expand and simplify.
(x 6)(x + 2)
Distributive Property
Example 2
Property
Find the Product of Two Binomials Using the Distributive
Expand and simplify.
a)
Lesson 5
The x-Intercepts of a Quadratic Relation
Factor.
x2 + 15x + 36
x2 5x - 14
5x2 + 30x - 135
Compare the Equation of a Quadratic Relation to Its Graph
1. a) Graph the quadratic relation y = x2 + 10x + 16. What are the x-intercepts?
a) Factor the exp
Lesson 4
The Quadratic Relation y = a(x h)2 + k
1. Write an equation for the parabola graphed with the solid line.
2. Describe each of the following parabolas compared to y = x2.
a) y = - 0.4(x + 5)2
b) y = 10(x 8)2
c) y = -x2 + 2
d) y = -(x + 3)2 + 5
e)
Quadratic Relations. Tables of Values. Graphs.
Name:_
1.
Make a table of values for each relation, using integer values of x from -3 to 3.
Graph the relationships.
a) y = x2
x
y
-3
-2
-1
0
1
2
3
b) y = 2x2
x
y
-3
-2
-1
0
1
2
3
c) y = x2 + 2x + 3
x
y
-3
-2
Worksheet: Quadratic Relations
Name:_
1.
Complete each table. Is the relation linear? Is the relation quadratic?
a) y = -3x + 7
Graph the relation.
b) y = x2 2x + 1
Graph the relation.
2.
Complete each table:
a) y = 2x + 1
b) y = 3x2 6x
3.
Is a quadratic
MBF 3C
Lesson 6
Solve Problems Involving Quadratic Relations
Graph the relation y = -x2 + 4x + 5 by finding the zeros and the y-intercept and determining the
maximum or minimum.
The graph of a quadratic relation is symmetrical. That means that if a vertic
Lesson 1
Modelling with Quadratic Relations
Investigate
Pp. 168 - 169
1. Complete the table.
Side Length of Square Farm
Field (m)
Area of Farm Field (ha)
Number of Bags of Fertilizer
Needed
100
1
6
200
4
24
300
9
400
16
500
25
600
36
2.
Line Scatter Plot
Lesson 5
Measures of Spread
Measures of central tendency are values around which a set of data tends to cluster.
However, to analyze a set of data, it is useful to know how spread out the data are.
Measures of spread describe how the values in a set of da