This document discusses the standard form of quadratic equations, inequalities, and functions. It provides examples of each and discusses key concepts such as the discriminant, product and sum of roots, tables of values showing the relationship between x and y, and using the quadratic formula to solve equations. It also demonstrates finding the vertex, axis opening, and other properties of quadratic functions given their equation.

1. Good
Morning

2. Standard Form
What is the
standard form
of Quadratic
equation?

3. 𝑥2
+ 4𝑥 + 4 = 0
Examples
𝑥2
+ 16𝑥 = 0
25 = 𝑥2

4. Standard Form
What is the
standard form
of Quadratic
Inequalities?

5. 𝑥 + 1 𝑥 − 1 > 0
Examples
(𝑥 − 3)(𝑥 + 2) < 0
2𝑥2
− 3𝑥 − 2 > 0

6. Standard Form
What is the
standard form
of Quadratic
Function?

7. 𝑦 = 𝑥2
− 8𝑥 + 15
Examples
2(𝑥 − 3)(𝑥 + 2) = 𝑓(𝑥)
𝑦 = 2𝑥2
− 6𝑥 − 5

8. Table of values
X 0 1 2 3 4
y 5 6 7 8 9

9. Table of values
X 0 1 2 3 4
y 0 1 4 9 16

10. Table of values
X 0 1 2 3 4
y 0 4 16 36 64

11. Table of values
X 0 1 2 3 4
y 2 1 -2 -7 -14

12. Discriminant
𝐷 = 𝑏2
− 4𝑎𝑐

13. 𝑟1 ∙ 𝑟2 =
𝑐
𝑎
Product of roots

14. 𝑟1 + 𝑟2 =
−𝑏
𝑎
Sum of roots

15. SolVE
𝑥2
+ 4𝑥 − 21 = 0 product sum Discriminant

16. SolVE
3𝑥2
− 8𝑥
= 4
product sum Discriminant

17. SolVE
2𝑥2
− 3𝑥 − 20 = 0 product sum Discriminant

18. Quadratic Function
Formula of
ℎ =
−𝑏
2𝑎
k =
𝑏2
− 4𝑎𝑐
4𝑎

19. EXAMPLE
𝑦 = −𝑥2
− 1 Vertex
(h, k)
axis opening

20. EXAMPLE
𝑦 = 𝑥2 + 𝒙 − 𝟔 Vertex
(h, k)
axis opening

21. EXAMPLE
𝑦 = 𝟏𝟎𝑥2 − 𝟏𝟑𝒙 − 𝟑 Vertex
(h, k)
axis opening