FACTORED FORM

A relation of the form is y= a(x-r) (x-s) is a quadratic function. The x-intercepts are r and s. To graph Factored Form we will need to find out the X-intercepts, Axis of Symmetry, and Optimal Value (to help find our vertex). For example, x-intercepts or zeros for the graph of the function  y= (x+6) (x-2) compared to y= a(x-r) (x-s). Therefore, the x-intercepts are -6 and 2. The x-intercepts are -6 and 2 because when you put something in the brackets the signs changes, so therefore the 6 has become positive and the 2 has become a negative. You can convert Factored Form to Vertex Form by finding the axis of symmetry (h value) which is add your 2 x-intercepts and divide it by 2. You also find the optimal value which is you k value. You will sub in the axis of symmetry into the original equation. You can also convert from Factored Form to Standard Form by expanding and simplfying.

 

Examples: