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.
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.
Airline High School
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.
A function is a relationship between variables (polynomial).
Before today, we have learned how to factor polynomials.
Can you think of some different ways that we factored?
Remember how to find the GCF?
Factor out a Greatest Common Factor.
Factor a difference of squares.
Factor trinomials where a=1.
Factor trinomials where a>1.
Factor by grouping.
Factor by graphing.
First, we make a table of values.
How do we graph ?
What do we know about the graph of a function when y = 0?
Now that we have our table, we can plot the values.
What happens between 1 and 2? How do you know?
Sketch the Graph!
You have to substitute a value BETWEEN 1 and 2 (say 1.5) to find the value of y.
What do the points (1, 0) and (2, 0) tell us about the function ?
They are the ZEROS of the function!
That’s right! y=(x – 2) (x – 3). Now, solve by factoring!
If you solved by factoring, then x=1 and x=2. VOILA!
How would you factor ?
Notice that your graph crosses the x-axis at x=1 and x=2
Then, we will use what is called the QUADRATIC FORMULA…..
What would happen if we could not factor a function to find the zeros?
Which is where we will start today.