1. Factored Form for Quadratic Relations

2. Example of Factored Form
𝑦=(𝑥−1)(𝑥−3)
Same as 𝑦= 𝑥 2 −4𝑥+3 and 𝑦= 𝑥−2 2 −1
factor
factor

3. 𝑦=(𝑥−1)(𝑥−3)

4. Example of Factored Form
𝑦=2(𝑥−1)(𝑥−3)
Same as 𝑦= 2𝑥 2 −8𝑥+6 and 𝑦= 2 𝑥−2 2 −2
factor
factor 𝑎

5. 𝑦=2(𝑥−1)(𝑥−3)

6. 𝑦=3(𝑥−1)(𝑥−3)

7. 𝑦=−(𝑥−1)(𝑥−3)

8. 𝑦=−2(𝑥−1)(𝑥−3)

9. 𝑦=−3(𝑥−1)(𝑥−3)

10. The General Factored Form
Coefficient is 1! Always! Srsly!
𝑦=𝑎(𝑥−𝑟)(𝑥−𝑠)
factor
factor
𝑟 and 𝑠 are the zeros/roots

11. Examples of Factored Form
Roots/Zeros
𝑦=3(𝑥−5)(𝑥−2)
+5, +2
𝑦=− 4 5 (𝑥+1)(𝑥−4)
−1, +4
𝑦=−𝑥(𝑥−2)
0, +2
𝑦= 𝑥+2 2
−2, −2

12. Why do we have more than one form?
Easy to see…
Vertex Form
𝒚=𝒂 𝒙−𝒉 𝟐 +𝒌
Factored Form
𝒚=𝒂(𝒙−𝒓)(𝒙−𝒔)
Standard Form
𝒚=𝒂 𝒙 𝟐 +𝒃𝒙+𝒄
Vertex 
Roots/Zeros
𝑦-intercept
Stretch or Compression Factor

13. Finding the Vertex
𝑦= 1 2 (𝑥−3)(𝑥+1)
𝑦= 𝑥−1 2 −2

14. Finding the Vertex 𝑦=4 𝑥−2 𝑥+5 Find the midpoint of the two roots
𝑦=4 𝑥−2 𝑥+5
Find the midpoint of the two roots
gives us the Axis of Symmetry
gives us the 𝑥-coordinate of the vertex
Evaluate the function at that 𝑥-value
gives us the 𝑦-coordinate of the vertex
Roots: (2,0) and (−5,0)
Midpoint of Roots: 2−5 2 ,0 = − 3 2 ,0
Evaluate function at 𝑥=− 3 2 :
𝑦=4 − 3 2 −2 −
𝑦=4 −
𝑦=−49