MCR3U1
U3L1
QUADRATIC FUNCTIONS
(and their Properties)
PART A ~ INTRODUCTION
A quadratic function can be identified by its equation, graph, or from a table of values.
degree:
Example 
the degree of a polynomial with a single variable is
the value of the highest exponent of the variable
a)
y = 4x – 5
Degree?
__________
b)
y = 2x2 + 5x – 8
Degree?
__________
The shape of the graph of a quadratic function is a ______________________________.
Example 
The table shows a relation between variables x and y:
x
y
0
1
2
3
4
5
6
1
6
9
10
9
6
1
First
Differences
Second
Differences
If the first differences are constant, the relation is __________________________________________.
If the second differences are constant, the relation is _______________________________________.
SUMMARY To identify a quadratic function:
Quadratic Functions
Table of Values
Graph
Equation
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VERTEX FORM
𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘
STANDARD FORM
𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
NOTE: V(h, k)
Axis of symmetry is x = h
NOTE: y–intercept is c
INTERCEPT FORM
𝑦 = 𝑎(𝑥 − 𝑟)(𝑥 − 𝑠)
NOTE: r & s are the x–intercepts
 the x–intercepts are also called the zeros or roots
 if a > 0, then the parabola opens up (concave up)
 if a < 0, then the parabola opens down (concave down)
PART B ~ EXAMPLES
Example 
a)
Sketch each of the following quadratic functions:
𝑦 = 2(𝑥 + 3)2 − 2
b)
𝑦 = −(𝑥 + 5)(𝑥 + 1)
y
y
x
x
direction of opening: ___________________
direction of opening: ___________________
vertex:
___________________
vertex:
___________________
axis of symmetry:
___________________
axis of symmetry:
___________________
domain:
___________________
domain:
___________________
range:
___________________
range:
___________________
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Example 
Determine an algebraic model for the given quadratic function:
Example 
Tony Roma was tossing his pizza dough in the air when it accidentally flew
out his window! Its height above the ground is modelled by the quadratic
function, ℎ(𝑡) = −5𝑡 2 + 20𝑡 + 25, where ℎ(𝑡) is the height in metres and
𝑡 is the time in seconds.
a)
Determine the height of the window above the ground.
b)
Determine when the pizza dough hits the ground.
c)
Determine the vertex of the path of the dough.
d)
Determine the domain and range of the function.
HOMEWORK: p.145–147 #1–8, 11, 12 (think!), 13