what is a zero of a function?
DESCRIPTION
What is a ZERO of a function?. Students, you should move on to the next slide in order to learn an introduction about the zeros of a function. Many topics will already be familiar to you. Morgan White Airline High School Algebra I. - PowerPoint PPT PresentationTRANSCRIPT
What is a ZERO of a function?Morgan White
Airline High SchoolAlgebra I
Students, you should move on to the next slide in order to learn an introduction about the zeros of a function. Many topics will already be familiar to you.
NEXT
Cobb County Curriculum Standard M.ALGI.4.9 Quadratic Equation: Student will be able to solve quadratic equations using a variety of methods, including quadratic formula, factoring, completing the square, scientific or graphing calculator, or computer.
What is a function?
Before today, we have learned how to factor polynomials.
Can you think of some different ways that we factored?
NEXTBACK
A function is a relationship between variables (polynomial).
Ways to Factor….1. Factor out a Greatest Common Factor.
2. Factor a difference of squares.
3. Factor trinomials where a=1.
4. Factor trinomials where a>1.
5. Factor by grouping.
6. Factor by graphing.
NEXTBACK
Remember how to find the GCF?
Review Factor by Graphing
How do we graph ?
NEXTBACK
2 3 2y x x
First, we make a table of values.
X Y
-1 6
0 2
1 0
2 0
3 2
4 6
What do we know about the graph of a function when y = 0?
Review Factor by GraphingNow that we have our table, we can plot the values.
NEXTBACK
2 3 2y x x
X Y
-1 6
0 2
1 0
2 0
3 2
4 6
0
1
2
3
4
5
6
7
-2 -1 0 1 2 3 4 5
Review Factor by GraphingWhat happens between 1 and 2? How do you know?
NEXTBACK
2 3 2y x x
0
1
2
3
4
5
6
7
-2 -1 0 1 2 3 4 5
Sketch the Graph!
Review Factor by GraphingYou have to substitute a value BETWEEN 1 and 2 (say 1.5) to find the value of y.
Next BACK
2 3 2y x x
-1
0
1
2
3
4
5
6
7
-2 -1 0 1 2 3 4 5
Review Factor by GraphingWhat do the points (1, 0) and (2, 0) tell us about the function ?
Next BACK
2 3 2y x x
-1
0
1
2
3
4
5
6
7
-2 -1 0 1 2 3 4 5
They are the ZEROS of the function!
FactorHow would you factor ?
Next BACK
2 3 2y x x
-1
0
1
2
3
4
5
6
7
-2 -1 0 1 2 3 4 5
That’s right! y=(x – 2) (x – 3). Now, solve by factoring!
If you solved by factoring, then x=1 and x=2. VOILA!
Notice that your graph crosses the x-axis at x=1 and x=2
What would happen??
What would happen if we could not factor a function to find the zeros?
BACK
Then, we will use what is called the QUADRATIC FORMULA…..
Which is where we will start today.