MCR 3U1
Unit 3
Lesson 1: Properties of a Quadratic Function
Quadratic functions can be expressed in different algebraic forms:
Standard Form:
ax 2  bx  c
Factored Form:
a ( x  r )( x  s )
Vertex Form:
f ( x )  a ( x  h) 2  k
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If a is positive then the parabola opens upwards. If a is negative then the parabola opens
downwards.
The vertex is located at the point (h, k). If a is negative then the vertex is a maximum. If a is
positive then the vertex is a minimum.
The axis of symmetry is the x value of the vertex (or x = h).
The zeroes (x-intercepts) of the parabola can be found by writing the quadratic function in
factored form.
To calculate the y-intercept, substitute x = 0 into the quadratic equation.
Example 1: Determine the type of function
represented by the table of values, and then state
the algebraic equation for the function.
x
y
0
-32
1
-14
2
0
3
10
4
16
5
18
6
16
7
10
8
0
9
-14
1st Differences
2nd Differences
Example 2: Graph the function f ( x)  3( x  3) 2  3 . State the vertex, the axis of symmetry,
the y-intercept, the x-intercepts, the direction of the opening, the domain and the range.
MCR 3U1
Unit 3
Example 3: The height of a rocket above the ground is modeled by the quadratic function
h(t )  4t 2  32t , where h(t) is the height in metres t seconds after the rocket was launched.
a) Graph the quadratic function.
b) How long will the rocket be in the air? How do you know?
c) How high will the rocket be after 3 seconds?
d) What is the maximum height that the rocket will reach?