There are three steps into graphing in factored form

 

1) Finding the zeros

2) Finding the axis of symmetry 

3) Finding the optimal value

 

 

 

 

Example 1: Graph the following y= 3(x+3)(x-5)

 

 

Step #1: Find the zeros

 

y=3(x+3)(x-5)

x+3=0    x-5=0 

x=-3       x=5

 

Step #2: Find the Axis of Symmetry 

 

Recall; Add two x-intercepts and divide them by 2 *refer to vertex form*

 

AOS= -3+5

              2

 

AOS: 1

 

 

Step #3: Find the Optimal Value

*Sub the Aos into the orginal equation*

 

y= 3(1+3)(1-5)

y= 3(4)(-4)

y= -48

 

 

 

Example 2: Graph the following equation y=x2+6x+8(Simple Trinomial) 

[Remember to put this in factored form, but we have to solve for product and sum]    4 x 2 = 8

 y= (x+4)(x+2)                                                                                                                4 + 2 = 6

 

Step #1: Find the zeros

 (x+4)(x+2)=0

x+4=0   x+2=0

x=-4      x=-2

 

Step #2: Find the Axis of Symmetry 

 

AOS:  -4+(-2)

               2

 

AOS: -3

 

 

Step #3: Find the Optimal Value

y=x2+6x+8

y= (-3)^2+6(-3)+8

y= 9-18+8

y= -1 

 

 

 

Now lets try: 

 

a) 0= 2(x+6)(x-8)                                                         b) y= x2+10x+16                                     c) 0= 10(x-2)(x+7)

 

 

     

 

 

 

*Use desmos to check your answers*

 

Go to https://www.desmos.com/calculator