This document appears to be notes from a lesson on quadratic equations. It covers solving quadratic equations using different methods like factorisation, the quadratic formula, and completing the square. It also discusses using the discriminant to determine the number and type of solutions, including cases where there are two real solutions, a repeated root, or no real solutions. It includes examples of solving quadratic equations and finding discriminants. The lesson content suggests students will learn to solve and analyze quadratic equations using various techniques.

1. 1
Jun 1­03:09 p.m.
Quadratic equations
ax2
+bx +c = 0
by factorisation
using GDC
by formula
y = (x­2)2
y = ­ x 2
+ 1
y = x2
­ 2
y = x2
+ 3
y = (x ­ 3 )2
+5
y= ­ 2 x 2
+ 1

2. 2
May 29­06:50 p.m.
y= 3x(x­2) y= ­x(x­2)
y= x(x­2)
y= (x­1)(x+2)
y= 2(x­1)(x+2)

3. 3
Jun 1­03:09 p.m.
Quadratic Equations
By the end of the lessson you will be able to :
• Solve quadratic equations by different methods.
• Anticipate the number of solutions of a
quadratic equation by studying its discriminant.

4. 4
Jun 1­03:09 p.m.
Quadratic equations
by factorisation
using GDC
by formula
by completing the square

5. 5
Jun 1­03:09 p.m.
Solve the equation:

6. 6
Jun 1­03:09 p.m.
Solve the equation:

7. 7
Jun 1­03:09 p.m.
Solve the equation:

8. 8
Jun 1­03:09 p.m.
Use the quadratic formula to solve the equation:

9. 9
Jun 1­03:09 p.m.
Simplify and then use your GDC to solve the
equation:

10. 10
Jun 1­03:09 p.m.
Use your GDC to solve the equations:

11. 11
Jun 1­03:12 p.m.
Unusual quadratic equations:

12. 12
Jun 1­03:12 p.m.
Unusual quadratic equations:

13. 13
Jun 1­03:12 p.m.
Disguised quadratic equations:

14. 14
Jun 1­03:12 p.m.
Unusual quadratic equations

15. 15
Jun 1­03:12 p.m.
Unusual quadratic equations:

16. 16
Jun 1­03:10 p.m.
The quantity is called the
discriminant of the quadratic equation.
Δ > 0 ⇒
Δ = 0 ⇒
Δ < 0 ⇒
the equation has two real roots.
the equation has a repeated root.
the equation has no real roots.
qformula.wma

17. 17
Jun 1­03:11 p.m.
Δ > 0 Δ = 0
Δ < 0
Two different real roots
One repeated root
(or two equal roots)
No root.

18. 18
Jun 1­03:11 p.m.
Calculate the discriminant of the quadratic expression
. Hence show that
is always positive.

19. 19
Jun 1­03:12 p.m.
Find the possible values of the constant k such that the equation
has a repeated root.

20. 20
Jun 1­03:13 p.m.
Solve the equation

21. 21
Jun 1­03:13 p.m.
Solve the equation
, for 0o
≤ x ≤ 360o

22. 22
Jun 1­03:13 p.m.
Find the maximum area of a rectangle which has a
perimeter of 28 units.

23. Attachments
qformula.wma