*An equation in factored form can reveal a lot about the equation:*

*1. each factor gives us the value of the graph’s zeros(x-intercepts)***Ex. y= (x-3)(x+1)(x-4) Make y=0 and solve for x to find the zeros**

Values of zeros are x= 3,-1, 4

2. determines the number of zeros

2. determines the number of zeros

For example the same equation from above has three brackets or three zeros. This tells us the

**number of zeros in this equation is three**.

Ex. y= (x-3)(x+1)(x-4)

First zero- (x-3) =0

**x= 3**

Second zero(x+1) =0

**x= -1**

Third zero (x-4) =0

**x= 4**

3. helps us to determine the degree of the polynomial

3. helps us to determine the degree of the polynomial

In this example to determine the degree of a polynomial you must count all the x’s.

**Ex. y= -4(x+3) (x-2)^2(x+6) (x+2)**

We must

**take the exponent “2” into account**on the second bracket, when we are counting. In all there are

**four x’s, which means that this is a degree 4 polynomial.**

**4. the multiplicity(order) of each factor tells us how the graph interacts at the x-intercepts**

To find the order of each factor, it is the exponent after the brackets and if there is no exponent on bracket/brackets then the order is one.

**For example this equation y=(x-1)(x+2) has an order of one.**

Multiplicity of 1- a straight line travels through the zeros

Multiplicity of 2(4, 6, 8…) - bounces at the zeros

**Take this equation for example y=(x-1) ^2 (x+2) at the x-intercept x=1, it will bounce and a straight line will go through the other zero x= -2**

Multiplicity of 3(5, 7, 9…) - inflects at the zeros

**For this equation y=(x+1) ^3 (x-3), at the x-intercept x=-1 the line going through it will not go straight through but it will be inflected. However for the second zero x=3 the line will go straight through.**

Shanise, Can you please add to your labels such that your name and "scribe post" will also be included?Thanks.

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