​Quadratics

Graphing Factored Form

 

 

Steps 

 

1. Find the x-intercepts

• Set "y" to zero 

• In other words, isolate for "x" 

• Example: y=2(x+3)(x-9) Both expression in the brackets should equal to zero 

     (x+3) = 0  so, x= -3 and (x-9) = 0 so x=9 

Therefore the two x-intercepts would be (-3,0) and (9,0)

 

2. Use the zeroes to find the axis of symmetry/"x" value of vertex

• Formula:

     x= r+s

           2

• To find the axis of symmetry find the midpoint/average by adding the two x-intercepts then dividing that numer by two. 

• Example: 1) -3+9= 6     = 3

                           2     2

 

3. Plug in the axis of symmmetry("x" value of vertex) into the original equation

• Example:

     y=2(x+3)(x-9)

     y=2(3+3)(3-9)

     y=2(6)(-6)

     y=12(-6)

     y= -72

 

Therfore:

- The vertex is the axis of symmetry and the optimal value (x,y)

 

4. Plot the vertex and the two x-intercepts 

 

    Example:

    Vertex: (3,-72)

     X-intercepts: (-3,0) and (9,0)