MCF3M1
3.2
Relating the Standard and Factored Forms
Goal: Compare the factored form of a quadratic function with its standard form.
Read the problem on page 132.

Factored form is a quadratic function in the form f(x) = a(x – r) ( x – s)

Standard form is a quadratic function in the form f(x) = ax2 + bx +c

Zeros of a relation the value of x for which a relation has a value of zero. They are
also the x-intercepts of its graph.
Example 1

Connecting the standard and factored forms of quadratic functions
Compare the two functions: Using the table of values.
R(x) = (40 - x)(10 + x) and R(x)= -x2 +30x +400
a. Complete the table below.
Rachel’s Function
x
R(x) = (40 - x)(10 + x)
0
4
8
12
Andrew’s Function
x
0
4
8
12
16
16
20
20
b. Use Expanding and Simplifying the factored form

Find the zeros or x-intercepts of the graph

Find the axis of symmetry

Find the maximum value or y-coordinate of the vertex.
R(x)= -x2 + 30x +400
MCF3M1
Example 2 Selecting a factoring strategy to determine the vertex of a quadratic function

F(x) = 2x2 – 5x – 12
 Step 1 Factor, use guess and check or decomposition.
 Step 2 Find the zeros by equating them to zero.
 Step 3 Find the axis of symmetry
 Step 4 Find the y-coordinate of the vertex by substituting the xvalue.
 Sketch the graph
MCF3M1
Example 3
Solving Problem Using A Quadratic Function Model
The height of a football kicked from the ground is given by the function h(t) = -5t2
+ 20t, where h(t) is the height in metres and t is the time in seconds from its
release.
a) Write the function in factored form.
b) When will the football hit the ground?
c) When will the football reach its maximum height?
d) What is the maximum height the football
reaches?
e) Graph the height of the football in terms of time without using a table of
values.
Example 4
Representing a quadratic function in factored and standard forms from a
graph.
From the graph of this quadratic function, determine the function’s factored and standard
form.
Factored form:
Standard form:
Practise: p139 #3ab,4 ace,
5abc, 7ace,8bdf 12 ac, 14 show
your work