MCF 3M1
Date: _______________
Lesson 1 - The Vertex Form of a Quadratic Function
In Chapter 3, we compared the standard form of a quadratic function () with the factored form
of a quadratic equation ( f ( x)  a( x  r )( x  s ) ). Both forms can be used to obtain information
about a quadratic function.
What happens if we wanted to know more about a certain quadratic function? Can we find the
maximum value of a quadratic function using either standard or factored form? _____ Is it
possible to find the coordinate values of the vertex with either form? ______
Essentially, we need to look at a third form of a quadratic function to answer the questions above.
Our third form is called the vertex form ( f ( x)  a( x  h) 2  k ).
All three forms can tell us something particular about the function:
Factored Form
f ( x)  a( x  r )( x  s)
Standard Form
f ( x)  ax 2  bx  c
Vertex Form
f ( x)  a( x  h)  k
Zeroes
x  r , x  s
y-intercept
starting point
yc
2
Coordinates of the vertex (h, k)
Axis of Symmetry (x = h)
Example 1
Complete the following using the quadratic function: f ( x)  2( x  5) 2  3 .
a) Form: __________________
b) Opens: _________________
c) Min/Max: _______________
d) Vertex: ________________
e) Axis of symmetry: ________
f) Graph the function:
g) State the domain: ______________
h) State the range: _______________
MCF 3M1
Unit 4
Example 2
Determine the equation, in vertex form, of the graph on the
right.
Example 3
Determine the information that can be determined from each quadratic function.
a) f ( x)  ( x  2) 2  7
b) f ( x)  ( x  3)( x  4)
c) f ( x)  x 2  5x  10
Example 4
The height of a baseball can be modeled by the function f ( x)  4( x  3) 2  10 , where x is the
time in seconds and f(x) is the height in metres.
a) When does the baseball reach its maximum height?
b) What is the maximum height of the baseball?
c) At what height was the baseball hit?