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What is a ZERO of a function?

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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

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.

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What is a function?

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?

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Ways to Factor….

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.

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Review 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?

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Review Factor by Graphing

Now that we have our table, we can plot the values.

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Review Factor by Graphing

What happens between 1 and 2? How do you know?

Sketch the Graph!

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Review Factor by Graphing

You have to substitute a value BETWEEN 1 and 2 (say 1.5) to find the value of y.

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Review Factor by Graphing

What do the points (1, 0) and (2, 0) tell us about the function ?

They are the ZEROS of the function!

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Factor

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

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What would happen??

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.

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