Transcript Document

How do you identify the zeros of a
quadratic function that has a common
monomial factor in each term ?
For example: f(x)= 6x2 +9x
In this lesson you will learn
how to identify the zeros of a
quadratic function by
factoring out a common
monomial factor.
Let’sReview
Review
Let’s
f(x)= 6x2 + 9x
= 3x(2x+3)
Just like 5 and 7
are distinct
factors of 35…
35 = (5)(7)
3x and (2x+3) are distinct factors of the
expression 6x2 + 9x.
Let’sReview
Review
Let’s
The zeros of a function are the input values
that make the function equal zero.
f(x)=x–3
X=3
f(3)=0
Core Lesson
f(0)=0
Finding the zeros
f(x)=6x2 +9x
f(x)=3x(2x+3)
0= 3x(2x+3)
3x = 0
x=0
2x+3 = 0
-3 -3
2x = -3
3
x= 2
3
f(- )=0
2
Core Lesson
3
f(- )=0
2
f(x)=6x2 +9x
=3x(2x+3)
f(0)=0
Core Lesson
In general:
The zeros of the
function f(x)=ax(bx-k)
will be
k
x=0 and x=
b
f(x)= 10x2 -15x
= 5x(2x-3)
Core Lesson
One more example:
f(x)=-2x2+8x
f(x)=-2x(x-4)
0=-2x(x-4)
Zeros: x=0 and x=4
Common
factor
= -2x
A Common
Let’s
Review Mistake
f(x)=2x2-6x
6
has only one zero: x= =3
2
The mistake is
not writing the
function in
factored form
to reveal both
zeros
x=0
f(x)=2x(x-3)
x=3
In this lesson you have learned
how to identify the zeros of a
quadratic function by
factoring out a common
monomial factor.
Guided
Practice
Let’s
Review
1. Write the function f(x)= 4x2-6x in
factored form to find zeros of the
function.
Guided
Practice
Let’s
Review
2. Write the function f(x)=-x2 -13x in
factored form to find zeros of the
function.
Extension
Let’s
ReviewActivity
Consider the equation r=s2 -st.
For what values of s and t does r=0?
Extension
Let’s
ReviewActivity
A cat jumps into the air from the ground with an
initial velocity of 10 feet per second.
a) Use the vertical motion model (h=-16t2 + vt + s) to
write an equation that gives the height (in feet) of
the cat as a function of time (in seconds).
b) After how many seconds does the cat land on the
ground?
Quick Quiz
Let’s
Review
Give the zeros of each function by
factoring:
1. f(x) = 7x2 -35x
2. f(x) = -2x2 +18x