Graphing From Factored Form

 

Step 1: Formula- y=a(x-r)(x-s)

 

When graphing factored form you always have to state the zeros, state the axsis of symmetry, state the optimal value, and state the direction of opening.

 

Step 2: State the zeros(x-intercepts)

 

-To find the zeros you have to set the "y" value to zero.

 

-Set both you brackets equal to zeros.

 

Example: y=-2(x+3)(x-1)

 

0=-2(x+3)(x-1)

x+3=0      x-1+0

  -3 -3        +1 +1

   x=-3        x+1

 (-3,0)       (1,0)

-Plot the two x-intercepts(zeros) onto the graph

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Step 3: State the axsis of symmetry

Formula: x=(r+s)/2

 

-When finding the axsis of symmetry your finding the point in between the two x-intercepts you found.

 

-Add both x-intercepts(zeros) found and divide by 2

 

Example: x=-3+1 = -2 =-1

                           2        2

Axsis of symmetry= -1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Step 4: State the optimal value

 

-In order to find the optimal value(vertex/y-int) you have to plug in the axsis of symmetry into the original equation

 

y=-2(x+3)(x-1)

axsis of symmetry=-1

 

y=-2(-1+3)(-1-1)

y=-2(2)(-2)

y=8

 

-Plot the y-int and then the graph is complete

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Step 5: State the direction of opening

 

-State weather the graph is opeing up or down

 

Example: The graph above is opening down