Quadratics

Graphing Factored Form 

 

Now that we have learnt about the factored form, and all the different components in the equation. Let us now take a look at how we would graph equations given in factored form. Please take a look at the video below to learn more about how to graph in factored form:

 

 

                                                                         Video: Graphing Factored Form

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary: The three key components while graphing in factored form are: the zeroes (roots), the axis of symmetry, and the optimal value. If we recall to our investigation of factored form, we will remeber that the equation is in the form: y=a(x-r)(x-s), where the x-value is the axis of symmetry, the y-value is the optimal value, and the r and s-values are the roots/zeroes. 

 

1. The Zeroes (roots/x-intercepts): The roots are found by setting each factor equal to 0. Hence, x-r=0 and x-s=0. 

2. The Axis of Symmetry: This is the midpoint of the two x-intercepts and is found by the following equation: x=(r+s)/2.

3. The Optimal Value: The optimal value is found by subbing in the axis of symmetry value into the equation.