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Investigating Factored Form

 

Throughout the quadratics unit, there are three forms we will be talking about: vertex form, factored form, and the standard form. In this section, we will be specifically focusing on investigating the factored form. Please take a look below and locate the factored form equation, as we will be using it as a starting point in investigating the factored form. 

Axis of Symmetry

Axis of Symmetry

Optimal Value

X-intercepts ("zeroes" or "roots")

X-intercepts ("zeroes" or "roots")

PART A: Exploring the x-intercepts ("zeroes" or "roots")

 

 

 

The x-intercepts in the factored form equation are identified as the r-value and the s-value. The x-intercepts are found by setting each "factor" equal to zero. 

PART B: Exploring the axis of symmetry

 

 

 

The axis of symmetry is the mid-point between the two x-intercepts. Therefore, in order to find the axis of symmetry, one needs to use the following equation: (r+s)/2.

PART C: Exploring the optimal value

 

 

 

The optimal value is found by subbing the axis of symmetry into the equation. 

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