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How do I graph in factored form?

Well to graph you need the basic things:

-The zeroes or x-intercepts (if any)

-The axis of symmetry (A.O.S) (Part of Vertex)

-The optimal value (Part of Vertex)

-The directon of opening 

If you have these then you have all the information you need to graph an equation

Video on  graphing in factored form  (Note: I used the same equation as shown so it can be a bit easier to understand)!

Let's say you have this equation in factored form: 

y=0.5(x+3)(x-9)

First of all you would find the zeros:

Ignore the "a" value which is 0.5 and take the terms in the brackets and make y=0

 

0=0.5(x+3)(x-9) 

(x+3)=0             So basically here you 

x=-3                   just make the terms

(x-9)=0              inside the brackets

x=9                    equal to zero.

Now we have the x-intercepts.

 

To find the Axis of Symmetry you would take the sum of the 2 x-intercepts and divide them by 2.  This will give you the x-value of the vertex.

A.O.S.= -3+9/2

          = 6/2

          = 3 

 

Now that we have the A.O.S.(x=3) we sub the value of it to our original equation:

y=0.5(3+3)(3-9)

y=0.5(6)(-6)       This gives us the y

y=0.5(-36)          co-ordinate of the 

y=-18                  vertex.

Now we have the vertex: (3,-18)

 

We are already given the a value so if it's postive the direction of opening will be upwards and if it's negative the direction of opening will be downwards. In this case the direction of opening is upwards. 

 

For the rest you would use the step pattern to graph the equation.

 

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