1. 4.4 Different Forms of Quadratic Expressions
Secondary Math 2
4.4 Different Forms of Quadratic Expressions

2. Warm Up
Use any method to solve. 𝑥 2 −13𝑥−68=0

3. 𝑥 2 −13𝑥−68=0

4. 𝑥 2 −13𝑥−68=0

5. 𝑥 2 −13𝑥−68=0

6. Recap of this unit so far…
We can solve quadratic equations using three different methods:
Factoring
Quadratic Formula
Completing the Square

7. What you will learn
The three different ways we can write a quadratic expression, and what they mean.

8. Standard Form: y=𝑎 𝑥 2 +𝑏𝑥+𝑐 Vertex Form: 𝑦=𝑎 𝑥−ℎ 2 +𝑘 Factored Form: 𝑦=𝑎(𝑥+𝑒)(𝑥+𝑓)

9. y-intercept: (0, c) Standard Form Standard form: 𝑓 𝑥 =𝑎 𝑥 2 +𝑏𝑥+𝑐
It is very easy to find the y-intercept from the standard form.
y-intercept: (0, c)

10. Factored Form
If we are interested in finding the x-intercepts of a quadratic, the factored form can help us find this. 𝑓 𝒙 =𝒂(𝒙+𝒆)(𝒙+𝒇) has x-intercepts at −𝑒, 0 , 𝑎𝑛𝑑 (−𝑓, 0).

11. 𝑓 𝑥 =𝑎 𝑥−ℎ 2 +𝑘 The vertex of the parabola will be at 𝒉, 𝒌 .
Vertex Form
𝑓 𝑥 =𝑎 𝑥−ℎ 2 +𝑘 The vertex of the parabola will be at 𝒉, 𝒌 .

12. Example
y-intercept:
(0, 12)
Consider the quadratic 𝑓 𝑥 =− 𝑥 2 −4𝑥+12 Factored form: 𝑓 𝑥 =−(𝑥+6)(𝑥−2) Vertex form: 𝑓 𝑥 =− 𝑥
vertex:
(−2, 16)
𝑥-intercepts: (-6,0), (2,0)

13. Example
Consider the quadratic 𝑓 𝑥 = 𝑥 2 −10𝑥+16 Factored form: 𝑓 𝑥 = 𝑥−8 𝑥−2 Vertex form: 𝑓 𝑥 = 𝑥−5 2 −9
𝑥-intercepts: (2,0), (8,0)
vertex:
(5, −9)

14. 1) 36 𝑎 2 −1=63

15. 2) 25 𝑟 2 −5=76

16. 3) 𝑛 2 +40=−13𝑛

17. 4) 𝑛 2 =3𝑛

18. 5) 9 𝑥 2 −19=0

19. 6) 11 𝑟 2 −2𝑟=6

20. 7) 𝑝 2 −10𝑝−24=0

21. 8) 𝑚 2 −14𝑚+33=0

22. Consider the following quadratic. 𝑥 2 +12𝑥+32=0
Exit Problem
Consider the following quadratic.
𝑥 2 +12𝑥+32=0
Solve it two different ways.
(Factor, complete the square, or quadratic formula).